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the order of a p-adic expansion of a rational function - Maple Help
Home : Support : Online Help : Mathematics : Group Theory : Numbers : P-adic : padic/orderp
padic[orderp] - the order of a p-adic expansion of a rational function
padic[lcoeffp] - the leading coefficient of a p-adic expansion of a rational function
Calling Sequence orderp(ex, p, x) lcoeffp(ex, p, x)
Parameters
ex - rational function p - irreducible (or square-free) polynomial or 1/x (or infinity) x - independent variable
Description
• The orderp command computes the order at p of the p-adic expansion of a rational function ex in x.
• The lcoeffp command computes the leading coefficient at p of the p-adic expansion of a rational function ex in x.
Examples
> $\mathrm{with}\left(\mathrm{padic}\right):$
> $\mathrm{expansion}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},{x}^{2}+2,x\right)$
${{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{1}}{+}\frac{{{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{2}}}{{}\left({{x}}^{{2}}{+}{2}\right)}{+}\frac{{{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{3}}}{{{}\left({{x}}^{{2}}{+}{2}\right)}^{{2}}}{+}\frac{{{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{4}}}{{{}\left({{x}}^{{2}}{+}{2}\right)}^{{3}}}{+}\frac{{{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{5}}}{{{}\left({{x}}^{{2}}{+}{2}\right)}^{{4}}}{+}\frac{{{{\mathrm{p_adic}}{}\left({{x}}^{{2}}{+}{2}{,}{0}{,}\left[{-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}{,}\frac{{4}}{{9}}{,}{-}\frac{{4}}{{81}}{+}\frac{{4}}{{81}}{}{x}{,}\frac{{4}}{{729}}{}{x}{-}\frac{{16}}{{729}}{,}{-}\frac{{4}}{{6561}}{-}\frac{{8}}{{6561}}{}{x}{,}{-}\frac{{20}}{{59049}}{}{x}{+}\frac{{44}}{{59049}}\right]\right)}_{{3}}}_{{6}}}{{{}\left({{x}}^{{2}}{+}{2}\right)}^{{5}}}{+}{\mathrm{O}}{}\left({{}\left({{x}}^{{2}}{+}{2}\right)}^{{6}}\right)$ (1)
> $\mathrm{orderp}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},{x}^{2}+2,x\right)$
${0}$ (2)
> $\mathrm{lcoeffp}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},{x}^{2}+2,x\right)$
${-}\frac{{1}}{{3}}{}{x}{-}\frac{{1}}{{3}}$ (3)
> $\mathrm{expansion}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},\frac{1}{x},x\right)$
$\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{1}}}{{}\left(\frac{{1}}{{x}}\right)}{+}\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{2}}}{{{}\left(\frac{{1}}{{x}}\right)}^{{2}}}{+}\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{3}}}{{{}\left(\frac{{1}}{{x}}\right)}^{{3}}}{+}\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{4}}}{{{}\left(\frac{{1}}{{x}}\right)}^{{4}}}{+}\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{5}}}{{{}\left(\frac{{1}}{{x}}\right)}^{{5}}}{+}\frac{{{{\mathrm{p_adic}}{}\left(\frac{{1}}{{x}}{,}{-}{1}{,}\left[{1}{,}{-}{3}{,}{4}{,}{4}{,}{-}{32}{,}{76}\right]\right)}_{{3}}}_{{6}}}{{{}\left(\frac{{1}}{{x}}\right)}^{{6}}}{+}{\mathrm{O}}{}\left({{}\left(\frac{{1}}{{x}}\right)}^{{5}}\right)$ (4)
> $\mathrm{orderp}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},\frac{1}{x},x\right)$
${-}{1}$ (5)
> $\mathrm{lcoeffp}\left(\frac{{x}^{3}+1}{{x}^{2}+3x+5},\frac{1}{x},x\right)$
${1}$ (6)
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# First Lecture
It’s was great seeing you this morning, and the attendance (esp. early birds) are really encouraging for me. So let me repeat what I said this morning here: if I’m still seeing so many early birds (like before 9:15), I’ll try to arrive every time by 9:15am and we can go through questions in the previous lecture or AOB~
So here comes the notes of day 1: wk1day1.pdf.
We set the backdrop of integral calculus as the area problem. Along with the tangent problem, these two constitute the two basic problems in Calculus, and one can roughly trace linkage to most ideas in integral and differential calculus respectively starting from here. (See Stewart’s p3-4)
We also explained how a sum of areas of adjacent rectangles $$f(x_i)\triangle x$$ can approximate the area under a curve defined by $$y = f(x)$$. The sum $$\sum_{i=1}^{n} f(x_i) \triangle x$$ is called a Riemann sum and the definite integral is defined to be $$\lim_{n\rightarrow\infty} \sum_{i=1}^{n} f(x_i) \triangle x$$
The whole bunch of symbols in the definition of definite integral means we are approximating the area under a curve by successively increasing the number of subdivisions n, and define the limiting value as the integral value, i.e. the area we’re looking for.
It’s important to note that $$x_i$$ had been chosen, initially, as the right end-point in the i-th interval counting from the left, and this hasn’t to be so, and lefties might prefer the left end points! But it is quite evident from the picture that choosing other points in the interval would not affect the limiting procedure describe above. For all details, please refer to the notes and the textbook, section 5.1 and 5.2.
Our lecture will continue on Tuesday Jan 8th, 9:30-11am (9:15am for early birds who wants to ask questions before the class) and I’ll aim to finish the proof and introduce the first physical interpretation of the area under a curve – distance.
I hope you liked the first lecture, and please let me know what you think by commenting below!
Posted in Lecture
###### 4 comments on “First Lecture”
1. Paniz Banki says:
Thank you for reviewing the stuff we went over in class, and most important what we will be doing in the next class. It makes everything more clear and organize.
• simontse says:
Thank you for your comment, and bringing me to attention that previewing what we’ll do in the next class. Now I find it all the more important to keep orientating you all in the teaching flow.
2. Manolito Pimentel says:
I also just wanted to say thanks for making this blog! It really makes a difference having this kind of up-to-date resource available!
• simontse says:
Thanks, and please then use it more (and Piazza too!), and give me feedback to improve. I’m also learning to teach, and your feedback mean a lot! (Especially if you find the pace going too fast, or something is presented in a confusing way!)
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5.3 Binomial distribution - university of calgary - base content (Page 5/30)
Page 5 / 30
Try it
A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. State whether this is binomial or not and state why.
This is not binomial because the names are not replaced, which means the probability changes for each time a name is drawn. This violates the condition of independence.
References
“Access to electricity (% of population),” The World Bank, 2013. Available online at http://data.worldbank.org/indicator/EG.ELC.ACCS.ZS?order=wbapi_data_value_2009%20wbapi_data_value%20wbapi_data_value-first&sort=asc (accessed May 15, 2015).
“Distance Education.” Wikipedia. Available online at http://en.wikipedia.org/wiki/Distance_education (accessed May 15, 2013).
“NBA Statistics – 2013,” ESPN NBA, 2013. Available online at http://espn.go.com/nba/statistics/_/seasontype/2 (accessed May 15, 2013).
Newport, Frank. “Americans Still Enjoy Saving Rather than Spending: Few demographic differences seen in these views other than by income,” GALLUP® Economy, 2013. Available online at http://www.gallup.com/poll/162368/americans-enjoy-saving-rather-spending.aspx (accessed May 15, 2013).
Pryor, John H., Linda DeAngelo, Laura Palucki Blake, Sylvia Hurtado, Serge Tran. The American Freshman: National Norms Fall 2011 . Los Angeles: Cooperative Institutional Research Program at the Higher Education Research Institute at UCLA, 2011. Also available online at http://heri.ucla.edu/PDFs/pubs/TFS/Norms/Monographs/TheAmericanFreshman2011.pdf (accessed May 15, 2013).
“The World FactBook,” Central Intelligence Agency. Available online at https://www.cia.gov/library/publications/the-world-factbook/geos/af.html (accessed May 15, 2013).
“What are the key statistics about pancreatic cancer?” American Cancer Society, 2013. Available online at http://www.cancer.org/cancer/pancreaticcancer/detailedguide/pancreatic-cancer-key-statistics (accessed May 15, 2013).
Chapter review
A statistical experiment can be classified as a binomial experiment if the following conditions are met:
1. There are a fixed number of trials, n .
2. There are only two possible outcomes, called "success" and, "failure" for each trial. The letter p denotes the probability of a success on one trial and q denotes the probability of a failure on one trial.
3. The n trials are independent and are repeated using identical conditions.
The outcomes of a binomial experiment fit a binomial probability distribution. The random variable X = the number of successes obtained in the n independent trials. The mean of X can be calculated using the formula μ = np , and the standard deviation is given by the formula σ = .
Formula review
X ~ B ( n , p ) means that the discrete random variable X has a binomial probability distribution with n trials and probability of success p .
X = the number of successes in n independent trials
n = the number of independent trials
X takes on the values x = 0, 1, 2, 3, ..., n
p = the probability of a success for any trial
q = the probability of a failure for any trial
p + q = 1
q = 1 – p
The mean of X is μ = np . The standard deviation of X is σ = $\sqrt{npq}$ .
Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.
In words, define the random variable X .
X = the number that reply “yes”
X ~ _____(_____,_____)
What values does the random variable X take on?
0, 1, 2, 3, 4, 5, 6, 7, 8
Construct the probability distribution function (PDF).
x P ( x )
On average ( μ ), how many would you expect to answer yes?
5.7
What is the standard deviation ( σ )?
What is the probability that at most five of the freshmen reply “yes”?
0.4151
What is the probability that at least two of the freshmen reply “yes”?
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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# Recent questions tagged general-aptitude
1
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1 vote
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5
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1 vote
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1 vote
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If the proposition ‘Houses are not bricks’ is taken to be False then which of the following propositions can be True? All houses are bricks No house is brick Some houses are bricks Some houses are not bricks Select the correct answer from the options given below: b and c a and d b only c only
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1 vote
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1 vote
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1 vote
23
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1 vote
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# TrackedSymbols affected by CurrentValue. Another problem with SetDelayed(:=)+OwnVales in Initialization
It is MWE, only a Disk[] that should print "Click" when clicked.
Also "date... updating" should be printed on the first evaluation and on each update of variable enabled. (which is constant in this MWE)
In the Column there is another Dynamic object which shows current MousePosition. And this element is responsible for printing (flooding) "date... updating" even though enabled is not changing.
DynamicModule[{enabled = True, pos},
Column[{
Dynamic[Print[DateString[] <> " updating"];
EventHandler[Graphics@Disk[], {"MouseClicked" :> Print["Click"]}],
TrackedSymbols :> {enabled}]
,
Dynamic[pos]
}]
, Initialization :> (pos := MousePosition["Graphics"])]
I think I don't understand this and IMO it is not expected or desired behaviour.
When one put another Print next to Graphics you will see that it is in face whole Graphics updating.
So the question is:
If it's not a bug (I missed something) then how to recreate this MWE so it behaves correctly.
I think it may be (but not necessarily) related to Why does a heavy background slow LocatorPane from updating, even if only the locators are Dynamic?
p.s. Dynamic[Refresh[..., TrackedSymbols:>{enabled}]] behaves the same way.
Edit so at the end it seems to be more related to Button evaluation inside DynamicModule
-
Ah I finally understand, somehow I read constant as constantly, which is quite different :P. – Jacob Akkerboom Mar 5 '14 at 14:50
Hm see update, maybe it has something to do with DynamicModuleValues. – Jacob Akkerboom Mar 5 '14 at 15:18
(This is more of an extended comment until a better understanding evolves.)
Finally I've found the relevant MathGroup thread from old - apparently the behaviour is as old as the dynamic interactivity in Mathematica. At that time, Norbert Pozar introduced a really simple example to demonstrate the strange internals of DynamicModule when a symbol in an Initialization assignment sets OwnValues instead of DownValues with SetDelayed (Set is fine). Be aware, this will probably crash your kernel!
DynamicModule[{x}, 1, Initialization :> (x := Print["Should never see this."])]
However, changing the assignment to something[]:=... works as expected. Clearly, DynamicModule evaluates the symbol x internally, even if it is never used; and if the symbol has side effects, that can be catastrophic.
Bottom line: always use DownValues instead of Onwvalues when doing assignments inside Initialization code in DynamicModule. Like that:
DynamicModule[{x}, 1, Initialization :> (x[]:= Print["Should never see this."])]
Spelunking in the definition of DynamicModule, I've found that the problem is even more deeply embedded: it must be in DynamicModuleBox. The following example still crashes a fresh kernel:
CellPrint@Cell@BoxData@DynamicModuleBox[{x}, 1,
Initialization :> (x := Print["Should never see this!"])]
-
Great thread! Thanks. – Kuba Mar 6 '14 at 22:51
@Kuba Unfortunately, no one from WRI replied to that MG thread so the only option we have is to explore the definition of DynamicModule. – István Zachar Mar 6 '14 at 22:55
I've pined JohnFultz in chat yesterday. I would love to see an explanation. p.s. added example for clarity, hope you don't mind. – Kuba Mar 6 '14 at 22:57
p.s. OwnValues are ok with Set, worth adding in bottom line that it is in context of SetDelayed. – Kuba Mar 6 '14 at 23:03
Maybe this does what you want?
DynamicModule[
{enabled = True, pos},
Column[
{
Dynamic[
Print[DateString[] <> " updating"];
EventHandler[
Graphics@Disk[], {"MouseClicked" :> Print["Click"]}
]
]
,
Dynamic[pos[]]
}
]
,
Initialization :> (pos[] := MousePosition["Graphics"])
]
Really... trial and error.
-
That seems hopeful, doesn't it? I'm not exactly sure what you mean. – Jacob Akkerboom Mar 5 '14 at 15:09
Just talking :P it's something but it will not help me, the main issue is still there. Now testking your answer... – Kuba Mar 5 '14 at 16:16
So the answer is: never ever use SetDelayed for OwnValues purposes of DynamicModule variables. Why? Everything is crazy then. – Kuba Mar 5 '14 at 16:21
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JEE Advanced is a national level entrance exam held once a year by the seven zonal IITs with guidance from the Joint Admission Board (JAB). Download Solved Examples on Chemical Equilibrium. Previous Years AIEEE/JEE Mains Questions. As the JEE Advanced is one of the toughest exams in the country, it is expected from you to know every inch of the syllabus without fail. JEE Main Previous Year Papers: If you are looking for JEE Main previous year question papers, then you have come to the right place.With just a few days left for JEE Main 2020 (September session), it is time for candidates to properly get on with their exam preparations. Q. The equilibrium constant of this reaction is :- $\Delta_{f} \mathrm{G}^{\circ}[\mathrm{C}(\text { graphite })]=0 \mathrm{kJ} \operatorname{mol}^{-1} \Delta_{f} \mathrm{G}^{\circ}[\mathrm{C}(\text { diamond })]=2.9 \mathrm{kJ} \mathrm{mol}^{-1}$ NCERT NCERT Exemplar NCERT Fingertips Errorless Vol-1 Errorless Vol-2. The equation for the equilibrium constant of the reaction The thermal dissociation equilibrium of $\mathrm{CaCO}_{3}(\mathrm{s})$ is studied under different conditions. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. (D) $\Delta \mathrm{H}$ is independent of the catalyst, if any SHOW SOLUTION JEE Advanced Question Papers 2021 - The authorities shall release the JEE Advanced 2021 question papers online on the official website once the exam is conducted. Updated: August 18, 2019 — 1:07 pm $\mathrm{K}_{\mathrm{c}}=\frac{1}{\sqrt{\mathrm{K}_{\mathrm{c}}}}$, $\mathrm{K}_{\mathrm{c}}=\frac{1}{\sqrt{\mathrm{K}_{\mathrm{c}}}}$, Q. (in mol $\mathrm{L}^{-1}$) will be : The present boxset contains the last 40 Years’ (1979-2019) Chapterwise Solved Questions of IIT JEE Physics, Chemistry, and Mathematics, along with previous years’ solved papers of IIT JEE and JEE Main & Advanced. Problems Sheets are a collection of a question bank for IIT JEE Mains and Advanced. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. [AIEEE-2012] Answer & Solution : Chemical Equilibrium. JEE Main Previous Year Solved Questions on Chemical Kinetics. (4)$\mathrm{K}_{1}=\frac{1}{\mathrm{K}_{2}}=\frac{1}{\left(\mathrm{K}_{3}\right)^{2}}$ Download Solved Examples on Chemical Equilibrium. A vessel at 1000 K contains CO2 C O 2 with a pressure of 0.5 atm. 107 ratings. If you have solved these practice sets than definitely, you will feel confident after seeing a question from these sheet in your entrance exams.These sheets should be followed by Chemical Equilibrium Class Notes PDF. Hi, Thank you for valuable feedback. Which of the following are Lewis acids? JEE Main Previous Year Papers Questions With Solutions Chemistry Chemical and Lonic Equilibrium. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. The thermal dissociation equilibrium of $\mathrm{CaCO}_{3}(\mathrm{s})$ is studied under different conditions. Enjoy increased flexibility . Biology. $\mathrm{NO}(\mathrm{g}) \longrightarrow 1 / 2 \mathrm{N}_{2}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g})$ at the same temperature is :-, 8 mol of $\mathrm{AB}_{3}(\mathrm{g})$ are introduced into a 1.0 $\mathrm{d} \mathrm{m}^{3}$ vessel. Maths. 2016] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. 3. This video is highly rated by JEE students and has been viewed 10 times. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. By solving JEE Main January 2019 chapterwise questions with solutions will help you to score more in your IIT JEE examination. Students who solve the previous year question papers of JEE Main/Advanced understand better the trend of questions and topics asked in past exams. The solution is (2002) 1)not a buffer solution with p H < 7 2)not a buffer solution with p H > 7 3)a buffer solution with p H < 7 4)a buffer solution with p H > 7 Ans. (1)4 (2) 6 (3) 12 (4) 8 If you have solved these practice sets than definitely, you will feel confident after seeing a question from these sheet in your entrance exams.These sheets should be followed by Chemical Equilibrium Class Notes PDF. (3) $5.82 \times 10^{-2}$ atm A vessel at 1000 K contains $\mathrm{CO}_{2}$ with a pressure of 0.5 atm. (2) $1.94 \times 10^{-2}$ atm Nov 06, 2020 - CHEMICAL EQUILIBRIUM | Previous Year Questions From JEE MAINS & Advanced | JEE MAINS 2020 Chemistry JEE Video | EduRev is made by best teachers of JEE. If it dissociates as $2 \mathrm{AB}_{3}(\mathrm{g}) \square \quad \mathrm{A}_{2}(\mathrm{g})+3 \mathrm{B}_{2}(\mathrm{g})$ (D) $\mathrm{K}_{\mathrm{C}}<1$ Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. (B) At the start of the reaction $\Delta \mathrm{G}=\Delta \mathrm{G}^{0}+\mathrm{RT} \ln \mathrm{Q}$ These will help you get an idea and feel of the actual exam paper. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is Equilibrium Quotient or Mass Action Ratio: Consider the equilibrium. CHEMICAL EQUILIBRIUM | Previous Year Questions From JEE MAINS & Advanced | JEE MAINS 2020 Chemistry. Scroll down to download the JEE Advanced Equilibrium Important Questions available as free PDF downloads to enhance your study process. The equilibrium constant of this reaction is :-, Q. (3) –1 The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by $2 \times 10^{-6} \mathrm{m}^{3} \mathrm{mol}^{-1}$. I think u can do the best (1) 0.3 atm (2) 0.18 atm (3) 1.8 atm (4) 3 atm. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. If the total pressure at equilibrium is 0.8 atm, the value of K is :-, The equilibrium constant $\left(\mathrm{K}_{\mathrm{C}}\right)$ for the reaction $\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})$ at temperature T is $4 \times 10^{-4}$ The value of $\mathrm{K}_{\mathrm{c}}$ for the reaction. There are a total of 75 questions from all three subjects and for each subject, 100 marks are allotted. [JEE-Mains 2016] SHOW SOLUTION A Sethi. (2) $\frac{\mathrm{K}_{2} \mathrm{K}_{3}^{3}}{\mathrm{K}_{1}}$ If the total pressure at equilibrium is 0.8 atm, the value of K is :-. As the JEE Advanced is one of the toughest exams in the country, it is expected from you to know every inch of the syllabus without fail. All question are updating 2019 to 2020 and student want more difficulty question on jee advanced paper so candidate can contact our whatsapp mobile no. By solving JEE Main January 2020 chapterwise questions with solutions will help you to score more in your IIT JEE examination. At equilibrium . Click here to start: × Enroll For Free Now & Improve Your Performance. × Thank you for registering. Physics. Maths. (4). (A,B,D) Solutions. (b) AlCl 3 and SiCl 4. [JEE-MAINS(online)-2013] [JEE-MAINS(online)-2012] DDP questions with answers. For the reaction $\mathrm{SO}_{2(\mathrm{g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{g})} \square \mathrm{SO}_{3(\mathrm{g})},$ if $\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{C}}(\mathrm{RT})^{\mathrm{x}}$ where the symbols have usual meaning then the value of x is : (assuming ideality) (1) 36 (2) 3 (3) 27 (4) 2 $2 \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{2} \mathrm{O}_{2}(\mathrm{g}) \square 2 \mathrm{NO}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}),\left(\mathrm{K}_{4}\right)$ This Book contains Chapterwise & Topicwise Problems and solutions from 41 years JEE Advanced papers (1979-2019) Questions in every chapter are categorized into Sub Topics; It also Includes Problems and solutions for last 7 years JEE Main Papers (2013-2019) The best part of this books is Proper subjective solutions are given for each question; Drawback of this Book: Summary of every … (1) $\mathrm{K}_{1}=\sqrt{\mathrm{K}_{2}}=\mathrm{K}_{3}$ The equilibrium constant KP for this reaction at 298 K, in terms of, The INCORRECT statement among the following , for this reaction, is, The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are, IIT JEE chemistry previous question papers, JEE advanced previous year questions chapter wise, Atomic Structure -JEE Advanced Previous Year Questions with Solutions, JEE Main Previous Year Questions Topicwise, Atomic Structure Revision Video – Class 11, JEE, NEET, Ferromagnetic Substance – Magnetism & Matters | Class 12 Physics Notes, Paramagnetic Substances – Magnetism & Matters | Class 12 Physics Notes, Forces || Newton Laws Of motion || Class 11 Physics Notes. [JEE-MAINS(online)-2013] (B) At the start of the reaction, dissociation of gaseous $\mathrm{X}_{2}$ takes place spontaneously 1. (4) $\mathrm{K}_{1} \mathrm{K}_{2} \mathrm{K}_{3}$ $(4)-\frac{1}{2}$ (2) 0.02 The quiz is designed for Chemical Equilibrium chapter for JEE Main level. s independent of catalyst but dependent on temperature, $\mathrm{CaCO}_{3}(\mathrm{s}) \square \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g})$, For this equilibrium, the correct statement(s) is(are), (A) $\Delta \mathrm{H}$ is dependent on $\mathrm{T}$, (B) $\mathrm{K}$ is independent of the initial amount of $\mathrm{CaCO}_{3}$, (C) $\mathrm{K}$ is dependent on the pressure of $\mathrm{CO}_{2}$ at a given $\mathrm{T}$, (D) $\Delta \mathrm{H}$ is independent of the catalyst, if any, s independent of catalyst but dependent on temperature. Resonance Sheet Questions. (3) $\frac{\mathrm{K}_{1} \mathrm{K}_{2}}{\mathrm{K}_{3}}$ JEE Advanced Syllabus Weightage- The syllabus of JEE Advanced is vast, encompassing the topics of classes 11 and 12 from Physics, Mathematics, and Chemistry.Students preparing for the exam must know about JEE Advanced syllabus weightage to have an idea about the topics which are frequently asked or have more weightage in the exam. [JEE – Adv. [JEE-MAINS(online)-2012] JEE Main Previous Year Papers Questions With Solutions Chemistry Chemical and Lonic Equilibrium. Download JEE Main 2020 (Jan) Chapter wise solved questions for Chemistry in PDF format prepared by expert IIT JEE Teachers at Mathongo.com. 6 Chemical Equilibrium : Le chatelier Principle (JEE Main + JEE Advanced + NEET + AIIMS) - Duration: 42:31. The equilibrium constant for the reaction is, For the decomposition of the compound, represented as, For the reaction $\mathrm{SO}_{2(\mathrm{g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{g})} \square \mathrm{SO}_{3(\mathrm{g})},$ if $\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{C}}(\mathrm{RT})^{\mathrm{x}}$ where the symbols have usual meaning then the value of x is : (assuming ideality), The equilibrium constants at 298 K for a reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D, IIT JEE previous years questions chapter wise JEE Advanced Notes JEE Advanced Notes, Ionic Equilibrium – JEE Main Previous Year Questions with Solutions, JEE Main Previous Year Questions Topicwise, Atomic Structure Revision Video – Class 11, JEE, NEET, Ferromagnetic Substance – Magnetism & Matters | Class 12 Physics Notes, Paramagnetic Substances – Magnetism & Matters | Class 12 Physics Notes, Forces || Newton Laws Of motion || Class 11 Physics Notes. **This app is completely free!!! [JEE-MAINS 2014] Check 100 most important solved questions of Chemistry prepared after the detailed analysis of questions papers of JEE Main 2019 January exam. Find concise chapter notes of chapter Equilibrium including important concepts, formulae and some previous year solved questions for JEE Main and JEE Advanced … Chemical Bonding and Molecular Structure's Previous Year Questions with solutions of Chemistry from JEE Advanced subject wise and chapter wise with solutions Download India's Best Exam Preparation App. The book 41 years IITJEE Advanced + 17 years JEE Mains (/AIEEE) Chapterwise Solved papers of Physics, Mathematics and Chemistry are excellent books containing the chapterwise collection of past years JEE Advanced and Main/AIEEE questions.It has been published by Disha Publication. IONIC EQUILIBRIUM | Previous Year Questions From JEE MAINS & Advanced | JEE MAINS 2020 Chemistry The correct relation from the following is : But make questions on degree of dissociation In Ionic equilibrium, the ionic substance dissociates into their ions in polar solvents. (3), At equilibrium, 2mol of $\mathrm{A}_{2}$ are found to be present. If the ratio of the activation energies of the forward (E f) and reverse (E b) reactions is 2/3 then: (1) E f … (1) $38.8 \times 10^{-2}$ atm If the total pressure at equilibrium is 0.8 atm, the value of K is :- The entire syllabus of Class 11th and 12th has been comprehensive to ensure maximum understanding of the concepts. (A) Decrease in the total pressure will result in formation of more moles of gaseous X Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. JEE-Advanced previous year topic-wise solutions Crystal clear solutions for each & every question. $\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \square \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{K}_{3} \quad(\mathrm{C})$ 2.1k SHARES. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. (1) 1.182 (2) 0.182 (3) 0.818 (4) 1.818 in terms of $\mathrm{K}_{1}, \mathrm{K}_{2}$ and $\mathrm{K}_{3}$ is : (1) $\frac{\mathrm{K}_{1} \mathrm{K}_{3}^{2}}{\mathrm{K}_{2}}$, (2) $\frac{\mathrm{K}_{2} \mathrm{K}_{3}^{3}}{\mathrm{K}_{1}}$, (3) $\frac{\mathrm{K}_{1} \mathrm{K}_{2}}{\mathrm{K}_{3}}$, (4) $\mathrm{K}_{1} \mathrm{K}_{2} \mathrm{K}_{3}$, Q. (a) PH3 and BCl3. (2), Q. JEE Mains aspirants may download it for free, and make a self-assessment by solving the JEE Main Equilibrium Important Questions Chemistry. (4) (A) 14501 bar (B) 29001 bar (C) 58001 bar (D) 1405 bar Download JEE Advanced papers with solutions. (1) (II) $2 \mathrm{NO}_{2} \square \mathrm{N}_{2}+2 \mathrm{O}_{2}$ (I) $\mathrm{N}_{2}+2 \mathrm{O}_{2} \square 2 \mathrm{NO}_{2}$ JEE-Advanced Mathematics Mathematics Chapters : Download Link (PDF) Chapter 1 - 1. 41 YEAR (1979-2019) IIT JEE ADVANCED PAPER SOLUTION 19 YEAR (2002-2020) JEE MAIN (AIEEE) PAPER SOLUTION Every aspirant must check the JEE Main/Advanced previous year question papers to understand the nature of the exam. Free Question Bank for JEE Main & Advanced Chemistry Equilibrium Equilibrium state. (4) $4 \times 10^{-4}$ (1) 0.3 atm (2) 0.18 atm (3) 1.8 atm (4) 3 atm Physics . (C) $\mathrm{K}$ is dependent on the pressure of $\mathrm{CO}_{2}$ at a given $\mathrm{T}$ JEE Advanced Question Paper 2017. This video is highly rated by JEE students and has been viewed 10 times. IIT JEE Advanced Previous Year Questions Solution for Chemical Equilibrium. Furthermore, along with the IIT JEE Previous Year Papers for the past 10 years, we have also provided the Answer Key and Paper Analysis to make your preparation journey much smoother. IIT Kanpur) 8,835 views 42:31 $(3) \mathrm{K}_{1}=\frac{1}{\mathrm{K}_{2}}=\mathrm{K}_{3}$ SHOW SOLUTION At equilibrium, 2mol of $\mathrm{A}_{2}$ are found to be present. It has Objective questions, subjective questions, Comprehension and statement matching problems, Previous years questions of IIT JEE Mains and Advanced. Practicing JEE Advanced Previous Year Papers Questions of Chemistry will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. When the reaction is not at equilibrium this ratio is called ‘Q C ’ i.e., Q C is the general term used for the above given ratio at any instant of time. 4.9. The equilibrium constant $\left(\mathrm{K}_{\mathrm{C}}\right)$ for the reaction $\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})$ at temperature T is $4 \times 10^{-4}$ The value of $\mathrm{K}_{\mathrm{c}}$ for the reaction. Please check your email for login details. 4.9. JEE Advanced Syllabus Weightage- The syllabus of JEE Advanced is vast, encompassing the topics of classes 11 and 12 from Physics, Mathematics, and Chemistry.Students preparing for the exam must know about JEE Advanced syllabus weightage to have an idea about the topics which are frequently asked or have more weightage in the exam. (1) 50.0 NCERT NCERT Exemplar NCERT Fingertips Errorless Vol-1 Errorless Vol-2. AtoZ Chemistry : Rishi Sir (B.Tech. $\mathrm{K}_{\mathrm{p}}=\frac{(2 \alpha)^{2}}{(1-\alpha)} \times \frac{0.5}{(1+\alpha)}$, $\mathrm{K}_{\mathrm{p}}=\frac{(2 \alpha)^{2}}{(1-\alpha)} \times \frac{0.5}{(1+\alpha)}$, Q. SHOW SOLUTION IIT JEE Mains Previous Year Questions Solution for Ionic Equilibrium. JEE-Advanced previous year topic-wise solutions Crystal clear solutions for each & every question. … Equilibrium JEE previous year questions with solutions are given here. Save my name, email, and website in this browser for the next time I comment. This includes IIT JEE Past Questions Papers for Chemistry, Physics and Mathematics questions with solution. 1.M NaCl and 1 M HC1 are present in an aqueous solution. (1) [JEE – Adv. This document is highly rated by JEE students and has been viewed 2918 times. Chemistry. (1) $\frac{\mathrm{K}_{1} \mathrm{K}_{3}^{2}}{\mathrm{K}_{2}}$ Chemistry . (4) Also browse for more study materials on Chemistry … Scroll down to download the JEE Advanced Equilibrium Important Questions available as free PDF downloads to enhance your study process. This document is highly rated by JEE … Oct 14, 2020 - Previous Year Questions - Chemical Kinetics (IIT - JEE advanced) JEE Notes | EduRev is made by best teachers of JEE. • The chapters provide a detailed theory which is followed by Important Formulae, Strategy to solve problems, and Solved Examples. One mole of $\mathrm{O}_{2}(\mathrm{g})$ and two moles of SO2(g) were heated in a closed vessel of one litre capacity at 1098 K. At equilibrium 1.6 moles of $\mathrm{SO}_{3}$ (g) were found. Look into the Sample Papers of Previous Years . Megha Khandelwal. In reaction $\mathrm{A}+2 \mathrm{B} \square 2 \mathrm{C}+\mathrm{D}$, initial concentration of B was 1.5 times of |A|, but at equilibrium the concentrations of A and B became equal. 1.M NaCl and 1 M HC1 are present in an aqueous solution. JEE Advanced Previous Year Questions of Chemistry with Solutions are available at eSaral. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. Download Chemical Equilibrium DDP sets PDF. The standard state means that the pressure should be 1 bar , and substance should be pure at a given temperature. The solution is (2002) 1)not a buffer solution with pH < 7. [JEE-MAINS(online)-2012] Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. Thermal decomposition of gaseous $\mathrm{X}_{2}$ to gaseous X at 298 K takes place according to the following equation : The standard reaction Gibbs energy, , of this reaction is positive. Maths. [AIEEE-2011] JEE Advanced is a gateway for candidates seeking admission in bachelor’s programmes, integrated master’s programmes as well as dual degree programmes offered at 23 IITs including Indian School of Mines (ISM) Download JEE Main 2019 (Jan) Chapter wise solved questions for Chemistry in PDF format prepared by expert IIT JEE Teachers at Mathongo.com. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. Previous Year Questions. (1) 60 (2) 80 (3) 30 (4) 40 (B), Q. (3), (1) 0.3 atm (2) 0.18 atm (3) 1.8 atm (4) 3 atm, Q. askIITians offers JEE Advanced chapter wise past year paper of physics, Chemistry & Maths for JEE. If the reaction is started with 1 mol of the compound, the total pressure at equilibrium would be (c) PH3 and SiCl 4. Biology. ENROLL. Problems Sheets are a collection of a question bank for IIT JEE Mains and Advanced. If it dissociates as $2 \mathrm{AB}_{3}(\mathrm{g}) \square \quad \mathrm{A}_{2}(\mathrm{g})+3 \mathrm{B}_{2}(\mathrm{g})$, The value of Kp for the equilibrium reaction $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g}) \square 2 \mathrm{NO}_{2}(\mathrm{g})$ is 2 The percentage dissociation of $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{g})$ at a pressure of 0.5 atm is, $\mathrm{K}_{1}, \mathrm{K}_{2}$ and $\mathrm{K}_{3}$ are the equilibrium constants of the following reactions (I), (II) and (III), respectively, One mole of $\mathrm{O}_{2}(\mathrm{g})$ and two moles of SO2(g) were heated in a closed vessel of one litre capacity at 1098 K. At equilibrium 1.6 moles of $\mathrm{SO}_{3}$ (g) were found. Download eSaral App for Video Lectures, Complete Revision, Study Material and much more...Sol. Practicing past year question paper with answers will help candidate to score more marks in IIT JEE 2020 Exams. JEE Mains aspirants may download it for free, and make a self-assessment by solving the JEE Main Equilibrium Important Questions Chemistry. NCERT P Bahadur IIT-JEE Previous Year Narendra Awasthi MS Chauhan. SHOW SOLUTION Download Chemical Kinetics Previous Year Solved Questions PDF. SHOW SOLUTION Some of the CO2 C O 2 is converted into CO on the addition of graphite. (A) On decreasing $\mathrm{P}_{\mathrm{T}}\left[\mathrm{Q}=\frac{\mathrm{n}_{x} \mathrm{P}_{\mathrm{T}}}{\mathrm{n}_{\mathrm{x}_{2}} \mathrm{n}_{\mathrm{T}}}\right]$ Q will be less than Kp reaction will move in forward direction Contact Us JEE (Advanced) Office, Block No. JEE Main Previous Year Papers Questions of Chemistry With Solutions are available at eSaral. : \mathrm{R}=0.083 \mathrm{L} \text { bar } \mathrm{K}^{-1} \mathrm{mol}^{-1}\right), Q. Find all the NEET Chemistry important questions from the chapter Chemical Equilibrium with solutions to perform better in the exam here. Physics. 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simulate_diversification_model {castor} R Documentation
## Simulate a deterministic uniform speciation/extinction model.
### Description
Simulate a speciation/extinction cladogenic model for diversity over time, in the derministic limit. Speciation (birth) and extinction (death) rates can each be constant or power-law functions of the number of extant species. For example,
B = I + F\cdot N^E,
where B is the birth rate, I is the intercept, F is the power-law factor, N is the current number of extant species and E is the power-law exponent. Optionally, the model can account for incomplete taxon sampling (rarefaction of tips) and for the effects of collapsing a tree at a non-zero resolution (i.e. clustering closely related tips into a single tip).
### Usage
simulate_diversification_model( times,
parameters = list(),
start_time = NULL,
final_time = NULL,
start_diversity = 1,
final_diversity = NULL,
reverse = FALSE,
include_coalescent = FALSE,
include_event_rates = FALSE,
include_Nevents = FALSE,
max_runtime = NULL)
### Arguments
times Numeric vector, listing the times for which to calculate diversities, as predicted by the model. Values must be in ascending order. parameters A named list specifying the birth-death model parameters, with one or more of the following entries: birth_rate_intercept: Non-negative number. The intercept of the Poissonian rate at which new species (tips) are added. In units 1/time. birth_rate_factor: Non-negative number. The power-law factor of the Poissonian rate at which new species (tips) are added. In units 1/time. birth_rate_exponent: Numeric. The power-law exponent of the Poissonian rate at which new species (tips) are added. Unitless. death_rate_intercept: Non-negative number. The intercept of the Poissonian rate at which extant species (tips) go extinct. In units 1/time. death_rate_factor: Non-negative number. The power-law factor of the Poissonian rate at which extant species (tips) go extinct. In units 1/time. death_rate_exponent: Numeric. The power-law exponent of the Poissonian rate at which extant species (tips) go extinct. Unitless. resolution: Non-negative number. Time resolution at which the final tree is assumed to be collapsed. Units are time units. E.g. if this is 10, then all nodes of age 10 or less, are assumed to be collapsed into (represented by) a single tip. This can be used to model OTU trees, obtained after clustering strains by some similarity (=age) threshold. Set to 0 to disable collapsing. If left unspecified, this is set to 0. rarefaction: Numeric between 0 and 1, specifying the fraction of tips kept in the final tree after random subsampling. Rarefaction is assumed to occur after collapsing at the specified resolution (if applicable). This can be used to model incomplete taxon sampling. If left unspecified, this is set to 1. added_rates_times Numeric vector, listing time points (in ascending order) for a custom per-capita birth and/or death rates time series (see added_birth_rates_pc and added_death_rates_pc below). Can also be NULL, in which case the custom time series are ignored. added_birth_rates_pc Numeric vector of the same size as added_rates_times, listing per-capita birth rates to be added to the power law part. Added rates are interpolated linearly between time points in added_rates_times. Can also be NULL, in which case this option is ignored and birth rates are purely described by the power law. added_death_rates_pc Numeric vector of the same size as added_rates_times, listing per-capita death rates to be added to the power law part. Added rates are interpolated linearly between time points in added_rates_times. Can also be NULL, in which case this option is ignored and death rates are purely described by the power law. added_periodic Logical, indicating whether added_birth_rates_pc and added_death_rates_pc should be extended periodically if needed (i.e. if not defined for the entire simulation time). If FALSE, added birth & death rates are extended with zeros. start_time Numeric. Start time of the tree (<=times[1]). Can also be NULL, in which case it is set to the first value in times. final_time Numeric. Final (ending) time of the tree (>=max(times)). Can also be NULL, in which case it is set to the last value in times. start_diversity Numeric. Total diversity at start_time. Only relevant if reverse==FALSE. final_diversity Numeric. Total diversity at final_time, i.e. the final diversity of the tree (total extant species at age 0). Only relevant if reverse==TRUE. reverse Logical. If TRUE, then the tree model is simulated in backward time direction. In that case, final_diversity is interpreted as the known diversity at the last time point, and all diversities at previous time points are calculated based on the model. If FALSE, then the model is simulated in forward-time, with initial diversity given by start_diversity. include_coalescent Logical, specifying whether the diversity corresponding to a coalescent tree (i.e. the tree spanning only extant tips) should also be calculated. If coalescent==TRUE and the death rate is non-zero, then the coalescent diversities will generally be lower than the total diversities. include_event_rates Logical. If TRUE, then the birth (speciation) and death (extinction) rates (for each time point) are included as returned values. This comes at a moderate computational overhead. include_Nevents Logical. If TRUE, then the cumulative birth (speciation) and death (extinction) events (for each time point) are included as returned values. This comes at a moderate computational overhead. max_runtime Numeric. Maximum runtime (in seconds) allowed for the simulation. If this time is surpassed, the simulation aborts.
### Details
The simulation is deterministic, meaning that diversification is modeled using ordinary differential equations, not as a stochastic process. The simulation essentially computes the deterministic diversity over time, not an actual tree. For stochastic cladogenic simulations yielding a random tree, see generate_random_tree and simulate_dsse.
In the special case where per-capita birth and death rates are constant (i.e. I=0 and E=1 for birth and death rates), this function uses an explicit analytical solution to the underlying differential equations, and is thus much faster than in the general case.
If rarefaction<1 and resolution>0, collapsing of closely related tips (at the resolution specified) is assumed to take place prior to rarefaction (i.e., subsampling applies to the already collapsed tips).
### Value
A named list with the following elements:
success Logical, indicating whether the simulation was successful. If the simulation aborted due to runtime constraints (option max_runtime), success will be FALSE. total_diversities Numeric vector of the same size as times, listing the total diversity (extant at each the time) for each time point in times. coalescent_diversities Numeric vector of the same size as times, listing the coalescent diversity (i.e. as seen in the coalescent tree spanning only extant species) for each time point in times. Only included if include_coalescent==TRUE. birth_rates Numeric vector of the same size as times, listing the speciation (birth) rate at each time point. Only included if include_event_rates==TRUE. death_rates Numeric vector of the same size as times, listing the extinction (death) rate at each time point. Only included if include_event_rates==TRUE. Nbirths Numeric vector of the same size as times, listing the cumulative number of speciation (birth) events up to each time point. Only included if include_Nevents==TRUE. Ndeaths Numeric vector of the same size as times, listing the cumulative number of extinction (death) events up to each time point. Only included if include_Nevents==TRUE.
### Author(s)
Stilianos Louca
generate_random_tree, count_lineages_through_time
### Examples
# Generate a tree
max_time = 100
parameters = list(birth_rate_intercept = 10,
birth_rate_factor = 0,
birth_rate_exponent = 0,
death_rate_intercept = 0,
death_rate_factor = 0,
death_rate_exponent = 0,
resolution = 20,
rarefaction = 0.5)
generator = generate_random_tree(parameters,max_time=max_time)
tree = generator$tree final_total_diversity = length(tree$tip.label)+generator$Nrarefied+generator$Ncollapsed
# Calculate diversity-vs-time curve for the tree
times = seq(from=0,to=0.99*max_time,length.out=50)
tree_diversities = count_lineages_through_time(tree, times=times)$lineages # simulate diversity curve based on deterministic model simulation = simulate_diversification_model(times, parameters, reverse=TRUE, final_diversity=final_total_diversity, include_coalescent=TRUE) model_diversities = simulation$coalescent_diversities
# compare diversities in the tree to the simulated ones
plot(tree_diversities,model_diversities,xlab="tree diversities",ylab="simulated diversities")
abline(a=0,b=1,col="#A0A0A0") # show diagonal for reference
[Package castor version 1.6.8 Index]
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Learn Insta try to provide online math tutoring for you. (ii) the weight of metal B and the weight of the alloy. The angles of a triangle are in the ratio 3 :2 : 7. Question 3. Selina Publishers Concise Mathematics Class 10 ICSE Solutions Chapter 7 Ratio and Proportion (Including Properties and Uses) Ratio and Proportion Exercise 7A – Selina Concise Mathematics Class 10 ICSE Solutions. Question 8. New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 7 Ratio and Proportion and Unitary Method Self Practice 7A Solution (1) Express each of the following ratios in its simplest form. All the solutions of Ratio and Proportion (Including Properties and Uses) - Mathematics explained in detail by experts to help students prepare for their ICSE exams. If you have any doubts, please comment below. Answer: Ratio between the prices of scooter and a refrigerator = 4:1 Cost price of scooter = ₹45,000 Let the cost of scooter = 4x Cost of refrigerator = 1x According to condition, Cost of scooter > Cost of refrigerator ⇒ 4x- 1x = 45000 ⇒ 3x = 45000 x = $$\frac { 45000 }{ 3}$$ ⇒ x = ₹15000 .’. ICSE SolutionsSelina ICSE SolutionsML Aggarwal Solutions. Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Also, find the ratio of the number of females to the whole population. Divide 64 cm long string into two parts in the ratio 5 : 3. Find each angle. Solution: HCF of 66 and 18 is 6. (iv) 40 … We provide step by step Solutions of Exercise / lesson-6 Ratio and Proportion for ICSE Class-7 Concise Selina Mathematics. Answer, Two numbers are in the ratio 4 : 7. Answer: A’s age = 6 years 8 months = 6 x 12 + 8 = 72 + 8 = 80 months B’s age = 7 years 4 months = 7 x 12 + 4 = 84 + 4 = 88 months ∴ Ratio between them = 80 : 88 = 10 : 11 Amount = Rs. is 16. 320 y’s share =$$\frac { 5 }{ 9 }$$ of Rs. = 11 : … = 168 Let first number = 4x and second number = 7x Now, L.C.M. Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 7 Ratio and Proportion Ex 7B are helpful to complete your math homework. Solution: The ages of two boys A and B are 6 years 8 months and 7 years 4 months respectively. Question 1. Solution: a : b = 3 : 5. 40,000 respectively. Our Solutions contain all type Questions with Exe-6 A and Exe-6 B, to develop skill and confidence. Express each of the given ratio in its simplest form : Divide 64 cm long string into two parts in the ratio 5 : 3. Their sum is 168. Unitary Method (Including Time and Work) 8. Answer. = 16 ⇒ x = 16 ∴Required numbers = 5x and 9x = 5×16 and 9×16 = 80 and 144. Find the value of x in each of the following such that the given numbers are in proportion. Find the fourth proportional of, Question 3. Ratio and Proportion (Including Sharing in a Ratio) 7. Answer, Find the mean proportional between 810, find the second. Ratio and Proportion ICSE Class-7th Concise Selina Mathematics Solutions Chapter-6. Find the mean proportional between. Answer: Total weight of A and B metals = 10 gm A’s weight = 7.5 gm B’s weight = 10 – 7.5 = 2.5 gm, (i) Ratio between A and B = 7.5 : 2.5 = $$\frac { 75 }{ 10 }$$ : $$\frac { 25 }{ 10 }$$ =3:1, (ii) Ratio between B and total alloy = 2.5 : 10 = $$\frac { 25 }{ 10 }$$ : 10 ⇒ 25 : 100 = 1 : 4. Profit, Loss and Discount 10. (ii) the share of A and the share of B. Question 5. of 4x and 7x = 4 x 7 x x = 28x ∴ 28x = 168 x = $$\frac { 168 }{ 28 }$$ x = 6 ∴ Required numbers = 4x and 7x = 4 x 6 = 24 and 7 x 6 = 42. Answer, is divided between A and B in such a way that A gets half of B. Express each of the given ratio in its simplest form : Solution: Question 2. Find the fourth proportional to: (i) 1.5, 4.5 and 3.5 (ii) 3a, 6a2 and 2ab2. Find the numbers. If the ratio between the numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all. The ratio between two quantities is 3 : the first is Rs. Find the share of each. The various concepts which are discussed under Chapter 7 are increase (or decrease) in a ratio, composition of ratios, continued proportion, properties of proportion and direct applications. Question 9. 1080. Find the fourth proportional of Solution: Question 3. How many rupees will each get?Answer. Question 22. Answer, In a class, the ratio of boys to the girls is 7:8. Check whether the following quantities form a proportion or not ? is 168, find the numbers. Question 16. Answer, A plot of land, 600 sq m in area, is divided between two persons such that the first person gets three-fifth of what the second gets. 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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
Published by Pearson
# Appendix B - Sets - B Exercise Set - Page 987: 7
True
#### Work Step by Step
As 5 is an odd number, it is the element of the set that is given.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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# What are the chances that a spacecraft is hit by space junk?
If a rocket flies into space there is a possibility that it will encounter a piece of space garbage; even a small screw can be fatal.
What are the chances that such a collision really takes place? What about such an encounter with the ISS?
• If you apply no lower boundary to the size? Hundreds of impacts expected per hour. Virtually all of them will be barely above atomic scales, but ... no lower boundary supplied! You need to look at the size/risk vs. frequency spectrum. Which is a very big question. FluffyFlareon's answer below is a good start. Jun 26, 2021 at 7:26
• The indisputable answer: it is non-zero, steadily increasing and can reach an irreversible point (if a collision triggers a "Kessler syndrome") Jun 29, 2021 at 8:20
• Related story ESA spacecraft dodges large constellation(=Starlink) Jun 29, 2021 at 11:01
• I think number of issue have to clarify 1. Controller algorithm may one issue know days have many controlling mechanism have to mention PID, fuzzy logic, Deep learning(neural network) those controlling algorithm not much developed in hardware object detection, object kinematics determination, obstacle detection, sensor accuracy, interfacing issue....etc. 2. As you know universe expand above we expected so object navigation and detection major bottle-neck for that. 3. Time delay major issue in space, know days processor speed of our machine not much faster, command send from controller or comma Jul 7, 2021 at 12:12
• nd receive from sensor have delay at that moment the space craft collide with object. 4.In hardware point of view the sensor accuracy not much accurate, have tolerance issue, identification and analyzing performance issue. Jul 7, 2021 at 12:12
Heh. So it turns out, figuring out the answer to this is precisely what I do for a living.
1. It depends on how big an object you are worried about hitting. Are you worried about damaging wiring harnesses? Are you worried about causing a radiator leak? Punching a hole in the crew module? Annihilating the vehicle altogether? The larger the object, the less likely, in rather dramatic scale.
2. It depends on what orbit you fly in. Different altitudes and inclinations have drastically different debris populations.
3. It depends on how big your vehicle is. Bigger vehicles get hit more.
4. It depends on how long you fly. Stay in orbit 10 years, and you'll get hit with roughly 10 times as much stuff as you would if you stayed for one year.
On ISS, we typically write requirements along these lines:
The [piece of hardware] will not sustain damage from orbital debris that could create a [catastrophic hazard | subcomponent failure | other defined failure] with a probability of 0.xyz over XY years.
What exactly we write depends specifically on the hardware involved, how much we care about it, how much could station suffer if we lost it, etc.
New piece of critical structure? We'd specify a pretty stringent requirement, say, something more than 99% over a decade.
Wire harness for a Wi-Fi antenna for payloads? Maybe not so much, say, 95-98% per year.
A more stringent requirement makes the hardware and (and perhaps more importantly) its certification process more expensive.
• Do you have any sources for this answer? Jun 26, 2021 at 3:15
• The start of this answer reminds me of a question on scifi asking about growing potatoes after being stored for a long time, and the top answer starts with "I am a PhD Student in potato post-harvest physiology".
– pipe
Jun 26, 2021 at 21:45
• @DavidHammen Nothing public I can point to easily. Been doing this for about 8 years though. My last project was the solar arrays they just installed last week and yesterday. References for points 1 and 2 are scattered throughout other answers I've given on this site (maybe when I have more time -- possibly several weeks from now -- I can dig them up and repeat them here). 3 and 4 are just math. I'm deliberately not giving exact numbers we use so I stay away from releasing information that isn't mine to release. Jun 27, 2021 at 2:31
• @Dave In general, we try to write the requirements to span the hardware's expected design life. The meteoroid environment model is constant with time, but the orbital debris environment model includes variations from year to year to try to predict the growth in traffic as well as the effect of the solar cycle on upper atmosphere density. Going for at least 10 years helps us capture most of that variation in an average sense so we aren't reporting out best-case or worst-case values and extrapolating Jun 28, 2021 at 0:58
• @Tristan I understand. I've been in a similar boat with regard to questions I can answer. NASA would classify $\vec F = m \vec a$ as ITAR-restricted if they had their druthers, and the DoD would prefer to classify the same equation as TS/NOFORN. Jun 28, 2021 at 13:42
## Safety Integrity Level (SIL)
The way that we would conventionally test for and mathematically define the risks involved in space flight, including from debris, would be through SIL levels that describe the number of dangerous events that could acceptably occur in a single hour of space flight. This is very similar to avionics, railroad systems, and autonomous driving.
The number of events per hour is very small, on the order of micro or nano events / hr for the lowest SIL levels, and decreases as the SIL level becomes more hazardous. In other words, MTBF should be very high for failures that are catastrophic and result in loss of life or destruction of expensive property like a shuttle, satellite, probe, or station.
SIL Description Acceptable failure rate Acceptable MTBF
SIL 4 Catastrophic: eminent loss of life and complete destruction of shuttle/station; situation unreasonably uncontrollable 10-9 events/hr 109 hrs, or 114,000 years of space flight
SIL 3 Hazardous: possible loss of life and spacecraft; a very difficult situation to control 10-7 events/hr 107 hrs, or 1,140 years of space flight
SIL 2 Major: reduction in safety margins; perhaps leading to non-fatal injuries or damage to important mission systems unrelated to survivability 10-5 events/hr 105 hrs, or 11.4 years of space flight
Note that these are the ideal statistics and aren't reflective of real-world practice. Also, the number represent the aggregate time of space flight across all relevant spacecraft. Imagine testing an entire fleet of 5000 self-driving vehicles, each driving on highways and city streets for 1000 hrs for a total of 5,000,000 hrs, and you measure how many times that one of the cars was placed into a "catastrophic" situation that led to fatality or "hazardous" situation that could've led to fatality. Say the numbers are 1 and 4 for a full 5 incidents. Then the average failure rate would be 5 events/5,000,000 hrs of drive time, or 10-5 events/hr. This would probably not be considered successful based on aviation standards, but automotive manufacturers and regulators might interpret these figures acceptable. In space flight, designers and the aeronautic institutions that employ them are pretty conservative, so these wouldn't be "good enough" – the technical term is an "intolerable risk" as opposed to an "acceptable risk".
Obviously, some objects that are unmanned are treated differently from manned spacecraft, and probes, satellites, space stations, etc. will have different risk metrics. The above is a general outline.
## Managing Risk
So if these SIL metrics need to be met for a mission to be satisfactorily safe, what can be done, when random debris is floating around in near-Earth orbit? The key is to:
• reduce the probability of dangerous events occurring;
• as well as manage faults, failures, and disasters when they occur.
The US DoD has catalogued 27,000 pieces of debris in near-Earth orbit hurtling at speeds of about 17,500 mph around the planet; NASA's statistical analysis of sensor readings approximate that 23,000 of these are the size of a softball (d = 9.7 cm) or larger, and thus definitely large enough to cause a catastrophic event. In addition there are an estimated:
• 23,000 pieces > 10 cm (d), softball sized
• 500,000 pieces > 1 cm (d), marble sized
• 100,000,000 pieces > 0.1 cm (d), width of mechanical pencil graphite
The marble sized ones and anything smaller can't be reliably tracked.
The paths of these more massive debris are analyzed (diagram above), and given a conservatively large margin of error to make the likelihood of a collision decrease to 10-9 events/hr or thereabouts. This is probably based on statistical tests (diagram above), such as Monte Carlo simulations (or something comparable but computationally faster). In the unlikely event that one of the 23,000-27,000 large tracked objects strays too far from its predicted trajectory while monitoring it (diagram above) and comes possibly dangerously close to the spacecraft, NASA initiates a Debris Avoidance Procedure, possibly involving both automated and manual roles of maneuvering the spacecraft to safety, which is part of long-standing guidelines at NASA as a means to limit SIL 4 events from occurring to an acceptable failure rate / probability.
As for the smaller debris, contemporary ships are equipped with shielding and ideally redundant protection (diagram) and redundant critical systems and hardware in case small debris damages the principal shields or mission-critical components or subsystems. Redundancy greatly reduces the probability of failure and greatly increases the MTBF. These shields work for debris smaller than 1 cm.
## Mid-sized debris risks probability difficult to measure?
That leaves the 1 cm – 10 cm debris, the most deadly debris. These are large enough to breach shielding and yet are small enough to be untraceable.
In order to find the probability of a collision with these, we'd need to use historical data of how many hours all of spacecraft has flown versus how many collisions with these kinds of debris have happened. Unfortunately, the number of collisions is statistically insignificant. The other problem is that the number of pieces of debris has not remained static. For instance, in 2009, a commercial spacecraft carrying Iridium crashed into a latent Russian satellite, resulting in thousands of new pieces of debris. So the number of debris has not stayed static, making the probability calculations dependent on chronological time humanity's explored or used near-Earth space. This renders computations challenging:
• small number of collisions, essentially statistically insignificant
• time-varying amounts of dangerous 1 cm – 10 cm debris
Compare this to our example of testing a fleet of self-driving cars. We can easily (theoretically) scale this to tens of millions of hours testing and dozens of accidents. The probability of crashing is more or less static or at least mean-reverting across all of the cars because hazards of crashing are not continuously increasing or decreasing unless some variable – like snowfall – perverts the data, with disproportionate amounts of accidents occurring during snowy conditions and sensors failing to detect snow-covered signs.
There may be no satisfactory range of numbers to quantify the probability without substantial historical data of collisions, near collisions, number of hours of space flight time conducted since the beginning of space exploration, and approximate number of 1 cm – 10 cm debris across the entire timeline of space flight, use, and exploration. NASA might know all of this data. Even then, our detection of 10+ cm objects has improved, our spacecraft is (probably) more reliable now, so any (hypothetical) past collisions were more likely than they would be today, introducing yet another set of variables to make things even more unfeasible to compute, since these probabilities would rely on historic data that's skewed toward obsolete technology of the past.
• What does SIL stand for? Jun 26, 2021 at 2:54
• sorry, yeah, that means safety integrity level Jun 26, 2021 at 2:58
• Do you have any sources for this answer? What is the source for the table, and for the figure? Jun 26, 2021 at 3:13
• So is a "SIL level" a safety integrity level level? What's the highest level level of safety integrity level level? Can we take it to a new level level? Do you need a PIN number for this? Jun 26, 2021 at 3:29
• @OrganicMarble The description looks similar to IEC 61508, which defines 4 SILs, and is something like the bible for safety-critical and safety-related systems. Jun 26, 2021 at 11:13
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# representing graph python
Output : 3. So I am trying to understand Dijkstra's algorithm in python but I don't understand the graph clearly since I don't understand the real meaning of each sublist, I understand that certain numbers like 3, 4, 1 … Implement weighted and unweighted directed graph data structure in Python. This is done with the help of legend() function. The Adjacency Matrix. In mathematics, a graph is a way of representing relational data. Vertex A vertex is the most basic part of a graph and it is also called a node.Throughout we'll call it note.A vertex may also have additional information and we'll call it as payload. It has numerous packages and functions which generate a wide variety of graphs and plots. It along with numpy and other python built-in functions achieves the goal. Graphs¶. Also, read: Draw an arrow using matplotlib in Python… It is also very simple to use. Even though it is designed for more complex graph structures, networkx is fairly easy to adapt to a taxonomy, which is just a particular case of a graph. Python has the ability to create graphs by using the matplotlib library. Before we try to implement the DFS algorithm in Python, it is necessary to first understand how to represent a graph in Python. There are various versions of a graph. This box gives information about the different plots in the graph with different colors and line types. But the question arrises : Applications of Weighted Graphs Maps with weights representing distances. A graph $$G(V, E)$$ consists of a vertex set $$V$$, and an edge set $$E\subseteq V\times V$$.. Often vertices are referred to as nodes.. If the edges in a graph are all one-way, the graph is a directed graph, or a digraph. The above picture represents the graph having vertices and edges. Representing a graph. A graph may have directed edges (defining the source and destination) between two nodes, or undirected edges. A Graph consists of a finite set of vertices(or nodes) and set of Edges which connect a pair of nodes. Note: A rectangular box at the top left corner of the graph is called legend. Ultimately though, we see the adjacency list representation using a pure map type (such as a dict in Python) as the most intuitive and flexible. Representing a graph with an adjacency matrix. Additional nodes can be added to the graph using the add() method. ; Edge An edge is another basic part of a graph, and it connects two vertices/ Edges may be one-way or two-way. Box plot chart : A box plot is a graphical representation of statistical data based on the minimum, first quartile, median, third quartile, and maximum.The term “box plot” comes from the fact that the graph looks like a rectangle with lines extending from the top and bottom. Another less popular library for is anytree. One of the easiest ways to implement a graph is to use a two-dimensional matrix. It implements a simple but feature-rich tree data structure and is also battle-tested (it reached version 2.8.0, not so common for Python libraries). Following is the pictorial representation for corresponding adjacency list for above graph: 1. It’s useful to be familiar with many ways to represent graphs as you will encounter them everywhere. Directed Graph Implementation: In an adjacency list representation of the graph, each vertex in the graph stores a list of neighboring vertices. Therefore it is a special type of labeled graph in which the labels are numbers (which are usually taken to be positive). If the optional graph argument is provided it must be a dictionary representing a directed acyclic graph where the keys are nodes and the values are iterables of all predecessors of that node in the graph (the nodes that have edges that point to the value in the key). To the graph with different colors and line types create graphs by using the matplotlib library source and destination between. If the edges in a graph is to use a two-dimensional matrix ways... The add ( ) function be positive ) ( which are usually taken to be ). Achieves the goal graphs Maps with weights representing distances list of neighboring vertices about the different plots in graph! A graph, each vertex in the graph, and it connects two vertices/ edges may be or! In mathematics, a graph in Python, it is necessary to first understand how to represent a graph a! Line types representation of the graph using the matplotlib library connects two vertices/ edges may one-way... Graph is a special type of labeled graph in Python, it is a way of representing relational.! Different plots in the graph, each vertex in the graph, or a digraph Python has ability. Edges ( defining the source and destination ) between representing graph python nodes, or undirected edges adjacency. The help of legend ( ) method representing relational data is another basic part of a graph is use... Packages and functions which generate a wide variety of graphs and plots necessary first. It is a special type of labeled graph in Python is to use a two-dimensional matrix graphs and...., the graph stores a list of neighboring vertices to be positive.... Data structure in Python to the graph stores a list representing graph python neighboring vertices DFS algorithm in.... Use a two-dimensional matrix vertex in the graph stores a list of neighboring vertices stores... Maps with weights representing distances all one-way, the graph using the add ( ).! Graph in Python above picture represents the graph stores a list of neighboring vertices are numbers ( are. Legend ( ) method may have directed edges ( defining the source and destination ) between two nodes, undirected! Is a way of representing relational data graph is a special type of labeled graph in which the labels numbers... Graph are all one-way, the graph is to use a two-dimensional matrix edges in a graph may directed! In Python, it is a way of representing relational data wide variety of graphs and plots try. Adjacency list representation of the easiest ways to implement the DFS algorithm in Python gives information about the plots! In an adjacency list representation of the easiest ways to implement a graph all! Representing distances a two-dimensional matrix the easiest ways to implement the DFS algorithm in Python, it is a type! Is to use a two-dimensional matrix connects two vertices/ edges may be one-way or two-way another basic part a... Edges ( defining the source and destination ) between two nodes, or undirected edges with... Python, it is a directed graph, each vertex in the graph is special! Information about the different plots in the graph with representing graph python colors and line types directed graph Implementation in. Above picture represents the graph is a directed graph, and it connects two vertices/ edges be. Of legend ( ) method Edge an Edge is another basic part of a graph in Python is necessary first... The matplotlib library source and destination ) between two nodes, or undirected edges, it necessary! Way of representing relational data a digraph a special type of labeled in. Adjacency list representation of the graph, each vertex in the graph, vertex... Graphs by using the matplotlib library the labels are numbers ( which are usually taken be. A digraph, the graph having vertices and edges which the labels are numbers which! A two-dimensional matrix, and it connects two vertices/ edges may be one-way or two-way representing distances nodes. Graph is a directed graph data structure in Python or a digraph ) between two nodes, or undirected.... Unweighted directed graph Implementation: in an adjacency list representation of the graph with different colors and line types numbers. Representing distances numerous packages and functions which generate a wide representing graph python of graphs and plots nodes, undirected... Graph having vertices and edges undirected edges Edge an Edge is another basic part of a in. Python, it is a directed graph data structure in Python, it is a special type of labeled in. Wide variety of graphs and plots this box gives information about the different plots in the graph a... Represents the graph is to use a two-dimensional matrix easiest ways to implement a graph may directed. The matplotlib library is to use a two-dimensional matrix or two-way has the ability to create graphs by using matplotlib! Functions achieves the goal numpy and other Python built-in functions achieves the goal a! All one-way, the graph is a directed graph Implementation: in adjacency! Or two-way graph data structure in Python, a graph may have directed edges ( defining the source and )... The goal Edge is another basic part of a graph in Python, it is directed. Achieves the goal are all one-way, the graph with different colors and line types different. Different plots in the graph is to use a two-dimensional matrix weighted graphs Maps with weights representing distances graph different... In mathematics, a graph are all one-way, the graph, and it connects two edges! Is another basic part of a graph in Python a two-dimensional matrix undirected edges with numpy and Python! Are usually taken to be positive ) Implementation: in an adjacency list representation of the easiest to... Be positive ) each vertex in the graph with different colors and line types of graph! Source and destination ) between two nodes, or a digraph numbers ( which usually...
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# Invoking TCC FROM Perl 5.12
#### David McClelland
I want to execute a "dir /bf" command from within Perl. As the "f" option is a TCC option I need to invoke TCC.EXE instead of CMD.EXE. To do this I create the environment variable:
PERL5SHELL=C:\Program Files\JPSoft\TCMD12x64\tcc.exe
and then run the program:
#!perl -w
use strict;
use 5.12.0;
say \$ENV{PERL5SHELL};
my @lns=`dir /bf `;
die \$! if (\$!);
chomp @lns;
say \$_ foreach @lns;
When I do this I get the output:
C:\Program Files\JPSoft\TCMD12x64\tcc.exe
If I do not create the PERL5SHELL then cmd.exe is invoked and the command work as expected (After I change the command to `dir /b` ).
Am I doing anything obviously wrong here or is TCC simply different from cmd.exe in a way that perl can not capture the command output stream as expected?
I am running
TCC 12.01.44 x64 Windows 7 [Version 6.1.7600]
and ActiveState Perl 5.12.2
#### ebbe
I want to execute a "dir /bf" command from within Perl. As the "f" option is a TCC option I need to invoke TCC.EXE instead of CMD.EXE. To do this I create the environment variable:
PERL5SHELL=C:\Program Files\JPSoft\TCMD12x64\tcc.exe
and then run the program:
etc. etc.
This command works in cmd.exe:
tcc.exe /c dir /bf
Its output can be piped so I'd assume that it works with your perl program
#### David McClelland
This command works in cmd.exe:
tcc.exe /c dir /bf
Its output can be piped so I'd assume that it works with your perl program
You are right. I can remove the PERL5LIB environment variable and then use the line:
my @lns=`tcc /c dir /bf `;
and get the expected directory listing. The down side is
1) each call results in two command shells are invoked: cmd.exe and tcc.exe.
2) The current working directory is not passed on through to tcc
It would seem that either:
1) perl is incorrectly invoking tcc or is not hooking up the output pipe correctly. Perl does hook up to cmd correctly and cmd correctly captures the output from tcc and thus passes it back to perl.
or
2) tcc is not emulating cmd.exe exactly
or I suppose, both.
In any case thanks for the solution. I hadn't thought of invoking tcc from cmd.exe
David
#### Steve Fabian
---- Original Message ----
From: David McClelland
To: ESFabian@zenge.org
Sent: Friday, 2011. February 11. 16:24
Subject: RE: [Support-t-2604] Re: Invoking TCC FROM Perl 5.12
| Quote:
| Originally Posted by ebbe
| This command works in cmd.exe:
| tcc.exe /c dir /bf
| Its output can be piped so I'd assume that it works with your perl
| program
|
| You are right. I can remove the PERL5LIB environment variable and
| then use the line:
|
| my @lns=`tcc /c dir /bf `;
|
| and get the expected directory listing. The down side is
| 1) each call results in two command shells are invoked: cmd.exe and
| tcc.exe.
| 2) The current working directory is not passed on through to tcc
|
| It would seem that either:
| 1) perl is incorrectly invoking tcc or is not hooking up the output
| pipe correctly. Perl does hook up to cmd correctly and cmd correctly
| captures the output from tcc and thus passes it back to perl.
| or
| 2) tcc is not emulating cmd.exe exactly
|
| or I suppose, both.
|
| In any case thanks for the solution. I hadn't thought of invoking tcc
| from cmd.exe
Try to insert the current directory into the command invoking TCC (without knowledge of Perl I symbolically represented it below as "cwd"):
my @lns=`tcc /c dir /bf cwd`;
As to invoking TCC without passing through CMD.EXE, try the same Perl command format that would invoke any other program (esp. text mode one, not a graphics mode one), most likely requiring the full path of TCC.EXE in the command.
--
Steve
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# Measuring the surprise element of policy actions
Dear fellow community members,
Here is the excerpt from Bernanke and Kuttner (2005) that I need to apply to gather my data.
"A measure of the surprise element of any specific change in the Federal funds target can be derived from the change in the futures contract's price relative to the day prior to the policy action. For an event taking place on day d of month m, the unexpected, or "surprise", target funds rate change can be calculated from the change in the rate implied by the current-month futures contract. But because the contract's settlement price is based on the monthly average Federal funds rate, the change in the implied futures rate must be scaled up by a factor related to the number of days in the month affected by the change,
$$\Delta i^u = \frac{D}{D-d} (f_{m,d}^0 - f_{m,d-1}^0)$$
where $\Delta i^u$ is the unexpected target rate change, $f_{m,d}^0$ is the current-month futures rate, and $D$ is the number of days in the month. The expected component of the rate change is defined as the actual change minus the surprise, or
$$\Delta i^e = \Delta i - \Delta i^u$$
."
I need help applying the above formulas to the Australian Futures Index below. Say there is a surprise change by the RBA (Reserve Bank of Australia) on September 16, what would be the $\Delta i^u$ and $\Delta i^e$? Am i using the right data to measure this? Any help would be very much appreciated as I am very new to finance.
Your chart shows the prices of stock index futures. That is not what the text is talking about. The text is talking about futures on the overnight federal funds rate. In the US this would be FFU6 for September. I dont think an exact Australian equivalent exists.
• Hi @dm63 thank you for your answer. 2 questions: 1. Seeing your suggestion about the FFU6, I found that Australia has the 30-day intrabank cash rate futures (quandl.com/data/CHRIS/…). Can i use this instead? 2. You mentioned I can't use the stock index futures, was it because the prices there do not incorporate the market's expectation of future rates, while prices in FFU6 do?
– umm
Sep 17 '16 at 13:01
• Yes, I believe that is the analogous futures contract for Australia.
– dm63
Sep 18 '16 at 11:39
• On your second question, the futures contract needs to be directly related to the policy rate controlled by the central bank for this formula to work. The underlying instrument for the contract you specified is the Australian overnight cash rate , which is indeed the policy rate for the Reserve Bank of Australia.
– dm63
Sep 18 '16 at 11:42
• Thank you. My final question: On the website above for Australian intrabank cash rate futures, there was a surprise cut by the RBA in May 3 (25 basis point cut), the future price on the 2nd of May was 92.18 and on the 3rd of May became 92.28. Using the formula above, the unexpected change (surprise for the market) then is 0.11 (d=3d=3) which equals to 11 basis points? In other words, the market already expected a 14 basis points cut (25-11)?
– umm
Sep 21 '16 at 1:41
• That looks right
– dm63
Sep 22 '16 at 9:25
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6.7 Image formation by mirrors (Page 7/10)
Page 7 / 10
Why are diverging mirrors often used for rear-view mirrors in vehicles? What is the main disadvantage of using such a mirror compared with a flat one?
Problems&Exercises
What is the focal length of a makeup mirror that has a power of 1.50 D?
+0.667 m
Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm focal length telephoto lens?
(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature. (b) What is its power in diopters?
(a) $–1.5×{10}^{–2}\phantom{\rule{0.25em}{0ex}}\text{m}$
(b) $–66.7 D$
Find the magnification of the heater element in [link] . Note that its large magnitude helps spread out the reflected energy.
What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors .
+0.360 m (concave)
A shopper standing 3.00 m from a convex security mirror sees his image with a magnification of 0.250. (a) Where is his image? (b) What is the focal length of the mirror? (c) What is its radius of curvature? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors .
An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.167 cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by optometrists to measure the curvature of the cornea for contact lens fitting. The instrument used is called a keratometer, or curve measurer.)
(a) +0.111
(b) -0.334 cm (behind “mirror”)
(c) 0.752cm
Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. This is stated ${d}_{\text{i}}={\mathrm{–d}}_{\text{o}}$ , since this is a negative image distance (it is a virtual image). (a) What is the focal length of a flat mirror? (b) What is its power?
Show that for a flat mirror ${h}_{\text{i}}={h}_{\text{o}}$ , knowing that the image is a distance behind the mirror equal in magnitude to the distance of the object from the mirror.
$m=\frac{{h}_{\text{i}}}{{h}_{\text{o}}}=-\frac{{d}_{\text{i}}}{{d}_{\text{o}}}=-\frac{-{d}_{\text{o}}}{{d}_{\text{o}}}=\frac{{d}_{\text{o}}}{{d}_{\text{o}}}=1⇒{h}_{\text{i}}={h}_{\text{o}}$
Use the law of reflection to prove that the focal length of a mirror is half its radius of curvature. That is, prove that $f=R/2$ . Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.
Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in ${\text{W/m}}^{2}$ projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 W and has an area of $\text{100}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{2}$ , and that half of the radiated power is reflected and focused by the mirror.
$\text{6.82 k}{\text{W/m}}^{2}$
Consider a 250-W heat lamp fixed to the ceiling in a bathroom. If the filament in one light burns out then the remaining three still work. Construct a problem in which you determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor. The ceiling is 3.0 m high. The problem will need to involve concave mirrors behind the filaments. Your instructor may wish to guide you on the level of complexity to consider in the electrical components.
where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!
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# How do I solve this equation :$\bar{z}-iz²=-\sqrt{3}-3i$ without using identity way?
let $z$ be a complex number and $\bar{z}$ it's conjugate ,i would like
to solve this equation :$$\bar{z}-iz²=-\sqrt{3}-3i$$ without using identity way ?
Note :by identity way the solution is clear and is: $z= -\sqrt{3}$
Thank you for any help
• What is the "identity way"? Mar 20, 2016 at 13:49
• I meant by identity way The real part of equality of RHS is the same the real part of the LHS ,the same with imaginary part Mar 20, 2016 at 13:51
• You could do the same by using the absolute value and the argument. Mar 20, 2016 at 13:53
Hint you can do it by arguments . now argument if RHS is $2\pi-\tan^{-1}(\sqrt{3})=2\pi-\pi/3$ so argument of lhs needs to be the same so $\tan^{-1}(z^2/\bar{z})=2\pi-\pi/3$ but $z^2=z \times \bar{z}$ can you continue from here?
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# Scripting a visual comparison between the derivative and some finite scheme
I want to make an application where I can specify a function $f:\mathbb R\to \mathbb R$ and a dynamic value $n$ and get the function $\frac{f(x+\frac{1}{n})-f(x)}{\frac{1}{n}}$. I moreover want to compare it to $f'(x)$, i.e. plot it in the same graph.
I first tried it with $f(x):=x^m, m=2$ and used Listplot, but even here I got into some obsticles. Here is my attempt:
Table[((x+1/n)^m)-x^m)/(1/n),{m,1000,100}]
Function[x,#][Rangle[10]]&/@%
%/.{n->3}//N
Show[
Plot[3 x^2,{x,0,10}]
ListPlot[#]&/@%
]
If I do just ListPlot[#]&/@% instead of the last line, the I get all the plots, however it doesn't compare.
I'd also like to get away from $x^m$ and make an abstraction w.r.t. $f$, but my tries with Function fails. Is there a difference between Function[$x$,term] and $\lambda x.$term ?.
-
Something like With[{n = 1*^2, f = Function[x, x Exp[x]]}, Plot[{f[x], f'[x], n DifferenceDelta[f[x], {x, 1, 1/n}]} // Evaluate, {x, -1, 1}]]? – J. M. Jun 6 '13 at 8:03
Here's a way to approach this. Define the function f[x] and two versions of the derivative: the real derivative df and a numerical approximation appF.
f[x_] := x^3;
df[x_] = D[f[x], x];
appF[x_, h_] := (f[x + h/2] - f[x - h/2])/h
We can plot them all together
Plot[{f[x], df[x], appF[x, 1/2]}, {x, 0, 1}]
and see both how the derivative compares to the approximation, and also how the derivative(s) compare to the original function. Taking this a bit further, set up a Manipulate to control the h parameter in the approximation:
Manipulate[Plot[{df[x], appF[x, h]}, {x, 0, 1}], {h, 0.001, 1}]
Now h is controlled by the slider and you can see that it gets closer to the real derivative as h gets closer to zero. Here's a somewhat more visually appealing example:
f[x_] := Sin[x^3];
df[x_] = D[f[x], x];
appF[x_, h_] := (f[x + h/2] - f[x - h/2])/h;
Manipulate[Plot[{f[x], df[x], appF[x, h]}, {x, 0, 1}], {h, 0.001, 1}]
To change example functions, only the definition of f needs to change (and perhaps the region over which the plot is made). When I re-read your problem, I realized I used a slightly different formulation of the derivative apporximation. Here is the one that corresponds to your problem statement:
f[x_] := Sin[x^3];
df[x_] = D[f[x], x];
appF[x_, n_] := (f[x + 1/n] - f[x])/(1/n);
Manipulate[Plot[{f[x], df[x], appF[x, n]}, {x, 0, 1}], {n, 1, 100}]
which gives (more or less) the same results as above.
-
I'm not entirely clear on what your intention is, but are you looking for something like this?
fComp[f_, n_, x_] := {n*((f /. x -> (x + 1/n)) - f), D[f, x]}
Show[Plot[Evaluate[fComp[x^2, 3, x]], {x, 0, 100}]]
Show[Plot[Evaluate[fComp[Tan[x], 1, x]], {x, 0, 2 Pi}]]
Alternately, you can simplify the syntax of fComp if you don't mind passing pure functions:
fComp[f_, n_] := {n*(f[x + 1/n] - f[x]), D[f[x], x]}
Show[Plot[Evaluate[fComp[#^2 &, 3]], {x, 0, 100}]]
Show[Plot[Evaluate[fComp[Tan, 1]], {x, 0, 2 Pi}]]
There are two "tricks" to take note of here. First, functions can be passed as arguments, just like any other expressions in Mathematica. The second is the use of Evaluate[] to ensure that the value of x from Plot[] is passed to the function before Mathematica tries to plot it. You'll get errors about invalid variables, otherwise.
To compare values of n, you could do any of the following:
Show[Plot[Evaluate[fComp[#^2 &, #]], {x, 0, 1}]&/@Range[10]]
Table[Plot[Evaluate[fComp[#^2 &, n]], {x, 0, 1}],{n,1,10}]
Manipulate[Plot[Evaluate[fComp[#^2 &, n]], {x, 0, 1}],{n,1,10,1}]
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I'm trying to figure out how to get the odd and pages to display the current section name and the odd pages to display the title of the paper.
How do I accomplish this?
I'm using article and I have fancyhdr loaded.
-
Here's one possibility:
\documentclass[twoside]{article}
\usepackage{fancyhdr}
\usepackage{lipsum}% just to generate text for the example
\fancyhf{}
\pagestyle{fancy}
\title{Some Title}
\author{Some Author}
\makeatletter
\let\hdrtitle\@title
\makeatother
\begin{document}
\section{Test Section One}
\lipsum[1-10]
\section{Test Section Two}
\lipsum[1-10]
\end{document}
-
I noticed that the pages shift left and right (as if written for a book). How do I remove that feature? – AlanH Mar 31 '13 at 3:15
@AlanH I am not sure what do you mean with "pages shift left and right". Perhaps that inner/outer margins are different for even and odd pages? If this is so, then you could load the geometry package with the centering option: \usepackage[centering]{geometry}. If you meant other thing, please explain in a little more detail. – Gonzalo Medina Mar 31 '13 at 4:17
When I use your code, the section number will display. It's quite confusing because the section number and the page number are both in the header. How do I just display the section title without the numbering? – AlanH Mar 31 '13 at 8:12
@AlanH just now I saw your comment; I see you opened a new question, with this issue. I've provided an answer to this new question. – Gonzalo Medina Mar 31 '13 at 13:57
titleps is an intuitive alternative to fancyhdr which provides \*title macros the contain the sectional unit titles (in contrast to using article's \leftmark, that has no immediate context).
Pilfering an example structure from Gonzalo:
\documentclass[twoside]{article}
\usepackage{titleps,lipsum}% http://ctan.org/pkg/{titleps,lipsum}
\title{Some Title}
\author{Some Author}
\makeatletter
\let\hdrtitle\@title% To store the title after using \maketitle
\newpagestyle{main}{%
{\hdrtitle}{}{\thepage}} % odd
\makeatother
\pagestyle{main}
\begin{document}
\maketitle
\section{A section}
\lipsum[1-10]
\section{Another section}
\lipsum[1-10]
\end{document}
The main driver for setting headers/footers is given by
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### Help Support The Rocketry Forum:
#### BDB
##### Absent Minded Professor
I started in the mid 80's with a Challenger-1 Starter Set. Perusing my some old Estes catalogues online (wasting my morning at work) brought back a bunch of memories and helped me remember 22 of my childhood rockets. I'm sure there were more, but here is a partial list.
Challenger-1 Starter Set
Discovery Starter Set
Wizard
Mean Machine
Hercules
Challenger-3
Fox Fire
Stealth
SR-71 Blackbird
Ram Jet
Corsair
SDI Satellite
Ninja
Hawkeye
Exocet (mini scale combo pack)
IQSY Tomohawk (mini scale combo pack)
Helio*Copter
Magnum
Recruiter
S.W.A.T.
Strike Fighter
The Recruiter and Strike Fighter have survived the years and flew great earlier this month. The Magnum partially survived a cato on my first launch as a BAR and has since been completely rebuilt and upgraded.
#### dhbarr
##### Amateur Professional
Single unbuilt Mosquito.
#### jpummil
##### Well-Known Member
Wow! Great thread...really brings back memories. Just noticed that Estes has all of the old catalogs still available online: https://www.estesrockets.com/customer-service/full-catalog/
So, started around '75 with the obligatory "Deluxe Starter Kit" including an Alpha, launch pad, launch controller, wadding, etc.
Around that time, I also had an X-Ray, the Javelin/Super Flea combo pack, and a der Red Max. This phase of rocketry culminated in a build of the old "D" powered Renegade (the old red and Black one)....which ended up atop a huge oak tree. "Lucky" for me, there was a bunch of "viney" growth going up the tree that I could use to climb it. Never really noticed the "leaves of three" on said vines....you can probably SEE where this is going In the end, I never was able to recover the rocket, but DID get multiple cortisone shots to deal with an extreme case of poison ivy :eyeroll: I recall building and flying an X-Wing Fighter a few years after that. Flew beautifully, but was very prone to damage.
#### michaelrmonteith
##### Active Member
Wow thinking back. It was around 1977-80 that I built some of my first rockets. The Estes Vigilante, Black Brandt, and Marauder. I still have them and still flyable but getting in sad shape. Both the Marauder and Vigilante have had a ton of flights but need rebuilt. I'm in the process of rebuilding them. Kind of excited to get to see my childhood rockets look like they did when I first built them. I guess the hardest part will be the decals for them. Researching that a bit.
Michael
#### neil_w
##### Good at some things
TRF Supporter
Wow thinking back. It was around 1977-80 that I built some of my first rockets. The Estes Vigilante, Black Brandt, and Marauder. I still have them and still flyable but getting in sad shape. Both the Marauder and Vigilante have had a ton of flights but need rebuilt. I'm in the process of rebuilding them. Kind of excited to get to see my childhood rockets look like they did when I first built them. I guess the hardest part will be the decals for them. Researching that a bit.
Stickershock23 lists the Marauder, although the page for it seems incomplete so it's hard to tell the status. Also check this thread.
JimZ's site has a decent scan of the Vigilante decals. Mark at Stickershock could almost certainly do that one up for you as well, or you could print that one yourself if you're so inclined, since it's a simple black-on-clear decal.
#### GlennW
##### Well-Known Member
The only rockets I still have from my childhood fleet are the Estes Javelin (from the Javelin/ Super Flea combo pack) and the Alpha III which is in sorry shape and unflyable. I guess you could also count my LTV Scout which I got as a kid but did not build until adult years. Also had a Blue Bird Zero and Icarus which were lost to trees, etc.
Glenn
#### rstaff3
##### Oddroc-eteer
I barely remember all the kits I had back in the late 60's and early 70's. I do remember the Estes V2, Starlight and Big Bertha. All were bought locally. I scratched a lot even back then. Most notably, I had a couple of boost gliders that I built from plans. They flew great despite my lack of building skills and knowledge of what it took one to fly well. What's even weirder is I have only built two in recent years. Both from kits but, despite better...er...skills and vast info on the web, both were unstable. Go figure.
#### Todderbert
##### Well-Known Member
1987 was the year I started rocketry as a teen. Built a Wizard, Mosquito, Nova Payloader and a Hercules. I think I bought the stand and launcher separate. I started with a homemade launcher that used a 6volt lantern battery and a light switch, later on got the cool electron beam controller. I loved my Hercules model, though I lost it on its maiden flight. Don't know why but as a kid you want to see how high it can go. Always used the largest engines possible. Good memories none the less.
#### neil_w
##### Good at some things
TRF Supporter
• K-50 Interceptor: my all time favorite, and I did a really nice job on it I have to say.
• K-33 Trident: a tough build, but came out pretty good. I don't know if I ever got it fully decaled; for some reason I recall it finishing out its days all white. I can't imagine why I didn't decal it, because I always enjoyed decaling, and still do. Guess I'll never sort that out.
• K-27 Honest John: the folded paper spin nacelles defeated me, and I never put them on. But I believe I built and finished the rest of it (because I just remembered painting something olive drab, and it must have been that model)
• 1270 Nike X
• K-45 Astron Beta
• EAC Viper
• the aforementioned Saros
• K-1 Astron Scout; this just came back to me as I was typing this post
I'm gonna necro my own thread because other forum discussions have reminded me of one I missed: K-13 Falcon. Mine was painted up just like the catalog pic:
This is yet another rocket that I never got to fly. I also can't remember if I ever did glide testing. I do know I airfoiled the heck out of the wings though.
Geez it makes me sad that I let my parents give away all my rockets. Blame lies totally with me, I could have taken at least some of them if I cared to.
#### neil_w
##### Good at some things
TRF Supporter
Nice. How old were you when you got started?
#### Spitfire222
##### Well-Known Member
TRF Supporter
I unfortunately disposed of my childhood rockets quite recently, having successfully saved them in the closet of my room at my parent's house. Having not been touched for such a long time I figured I should get rid of them, completely unaware that I'd get back into it a year or two later. I very much regret the decision!
My first rocket was a USS America Starter Set (the red, black, and white scheme version) for Christmas '96. It was my most flown rocket back then, which was probably only a few more than a dozen flights since I couldn't get motors often. The rest of the fleet was:
-Estes Black Brant II (revisited as BAR)
-Estes Yankee (revisited as BAR)
-Estes Mosquito (CATO-ed on first flight)
-Estes Ninja (lost in a forest after a few flights)
-Estes Tornado x 2 (one was mine (lost on first flight), the other was my sister's, discarded when she cleaned out her room)
-Estes Mach 12
I actually did find a NIB USS America Starter Set on ebay and purchased it. I haven't build it yet, I might save it as my newborn son's first rocket when he's a bit older!
#### mbeels
##### Yes balsa
TRF Supporter
Nice. How old were you when you got started?
I think I was maybe 10 or 11? Some around age 15 I got into R/C airplanes, and then age 17 I got into ham radio and I've been cycling through those hobbies since.
Do you remember how old you were?
#### mbeels
##### Yes balsa
TRF Supporter
-Estes Yankee (revisited as BAR)
Ah yes, my brother had that rocket, and I'm pretty sure we lost it on a C6-7.
I actually did find a NIB USS America Starter Set on ebay and purchased it. I haven't build it yet, I might save it as my newborn son's first rocket when he's a bit older!
Nice find! I still have the nose cone from mine, but that's all.
#### neil_w
##### Good at some things
TRF Supporter
I think I was maybe 10 or 11? Some around age 15 I got into R/C airplanes, and then age 17 I got into ham radio and I've been cycling through those hobbies since.
Do you remember how old you were?
Probably about the same, but it's just a guess since there is no historical record of any kind and that was a looooong time ago. Conceivably could have been a bit younger, maybe 8 or 9.
#### Spitfire222
##### Well-Known Member
TRF Supporter
Ah yes, my brother had that rocket, and I'm pretty sure we lost it on a C6-7.
Unsurprising, considering how Yankee-type rockets are almost out of sight on an A8. I lost the Tornado on only a B6-4! Granted, it was a very windy day, and I launched into the low sun for a school demonstration....
Nice find! I still have the nose cone from mine, but that's all.
I think there were two on ebay at the time I got mine last year, so if you're interested, it might be worth it to check from time to time if more show up.
#### Stewman
##### Well-Known Member
TRF Supporter
As someone previously posted, this is a fun thread, and brings on lots of good memories, and a few not so good. My first rocket was the Alpha Starter kit, flew it July 19, 1967. Lost it to a tree, but salvaged the nose two years later when it fell out of the tree it found. But I was hooked, and Estes Industries received a lot of orders for a while as my lawn mowing money went into $5.00 orders so I could get a free kit. I had so many Gyroc's, I finally started using the parts to make a lot of the Estes plans that were sent with your order, or in the MRN and the various publications Estes had. Still have several of those early models that still fly after all these years. Also had some Centuri, AVI Astroport, MPC, CMR and FSI kits, among others. My first original design was built in 1968, I named it the Skyscraper II, and it still flies regularly. Cost me a whole$2.65 to build. I loved scale models, and finally saved up enough to get the Saturn V. Launched it while I was in college, and it crashed, destroying it completely. I now have two more, both the Estes and Apogee versions.
I was always pretty good about copying plans, making fin templates, etc., and have a file cabinet full of folders for all of my models. In 2001, I decided to recreate my original fleet of models, which turned out to be 46 total, (between 1967 and 1972). That has turned out to be quite a job, but I am over half-way there and hope to complete the rest of those models in the next couple of years. My line of work always had lots of hours involved so working on rockets wasn't always on the schedule. Won't bore you all with that list, but it includes a lot of classics. Now that I'm retired, I can devote much more time to my favorite hobby.
The Alpha will always be my favorite, but some others include the Big Bertha, Orbital Transport, Constellation, Cherokee D, and of course the Interceptor. My favorite Estes plan was the Starship Excalibur, which was circa 1968.
#### shockie
##### High Plains Drifter
1967-1973
Scout
X-Ray
Streak
Sprite
Sky Dart
Nighthawk
Space Plane
Falcon
Camroc
Spaceman
Trident
Gyroc
Birdie
Cox Little Joe II
MPC Flatcat
I also had about \$500 worth on unopened kits and 2 range boxes full of engines that I had purchased at NARAM-12 and 13 that my mom threw away around 1980. I had a Saturn V but I can't remember if it was Estes or Centuri
my 1st DIY model rocket was a BT-50 sized rocket I painted Purple because I was a fan of the Minnesota Vikings and Fran Tarkenten back then and their defensive line was called the Purple People eaters.... just 3 fins and a nose cone
For launchers my 1st was the Estes Red Electro-Launch, a Centuri LIA-77 with the Pro Firing Panel, a Centuri pneumatic launcher?, the Servo Launcher and later the COX Launcher and a MPC launcher with the ceramic blast deflector
I also had a full Vashon Rocket set.
Last edited:
#### Funkworks
##### Well-Known Member
I only had an Estes Alpha or an Alpha III. My last flight was on a C motor, and it landed in the woods.
Walking 1000 ft to look for it was too much for my patience back then so that’s when I quit the hobby. That and being bitten by a horsefly while looking for the rocket. Ouch.
#### TALON
##### Well-Known Member
1968 (13 YO): Estes ARCAS & the free Star Blazer.
1970 Estes Alpha, Aerobee 300 & Streak
1971 Estes Sky Dart, Gyroc & Sprint
Loved the blue engine tubes!
#### neil_w
##### Good at some things
TRF Supporter
1968 (13 YO): Estes ARCAS & the free Star Blazer.
1970 Estes Alpha, Aerobee 300 & Streak
1971 Estes Sky Dart, Gyroc & Sprint
Loved the blue engine tubes!
Still have any of them?
#### TALON
##### Well-Known Member
Still have any of them?
Lost/fatal zippers to all except the Sprint & skydart. had them till 1990. Did not launch them after 74. During a move the Fins/wings came off and since I deemed then not airworthy I threw them out. Wish I didn't now!
TRF Supporter
CA 1976
#### Tobor
TRF Supporter
My first rocket (built and lost) was an Estes Astron Scout, circa 73'. The fins were not quite straight and it had an atrocious paint job. Flew it on an "A" or "B" motor initiated with the very old-school "Red" BP fuse and no launch pad or launch rod.
From 73'~78'
These (In no particular order) are the ones I can remember...
Estes Kits
Scout
Astron Delta w/Camroc
Bomarc
Gyroc
Sprite
Big Bertha
Midget
RTF X-15
Andromeda
Space Shuttle
Centuri Kits
Taurus
Bandito
Groove Tube
Vector-V
Quasar Spaceship
Hummingbird
Fireflash
Moonraker
#### mbeels
##### Yes balsa
TRF Supporter
Flew it on an "A" or "B" motor initiated with the very old-school "Red" BP fuse and no launch pad or launch rod.
How did that go?
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7.7: Solution Equations: Weak Electrolytes
Learning Objectives
• Define weak electrolyte.
• Define recombination.
• Define equilibrium.
• Compare and contrast the definitions of non-, strong, and weak electrolytes.
A weak electrolyte is a solute that partially dissociates, or separates, into its constituent cations and anions during the solvation process. However, the cations and anions that result from the solvation of a weak electrolyte experience strong electrostatic attractions and often recombine to regenerate the solute molecule from which they were produced. Therefore, solutions that are generated through the solvation of weak electrolytes contain both neutral molecules and ions. Because an electrical current can only flow between ions, the resultant homogeneous mixtures will weakly conduct an electrical current, as illustrated in the third image that is shown in Figure $$\PageIndex{1}$$.
The dissociative behavior that is exhibited by a weak electrolyte is represented in the solution equation pattern that is shown below. Although a chemical change does not occur when a solution is formed, an arrow is used in a solution equation to indicate that solvation and, therefore, a physical change, has occurred. However, a standard "reaction" arrow, "$$\rightarrow$$," cannot be used to represent the solvation of a weak electrolyte, as this symbol indicates that transformations in the corresponding equation only occur in the "forward," or left-to-right, direction. As stated above, the cations and anions that result from the solvation of a weak electrolyte often recombine to regenerate the solute molecule from which they were produced. Therefore, the dissociation of weak electrolytes is reversible, and the arrow that is utilized to describe the recombination process must be oriented in the "backward," or right-to-left, direction in a solution equation. In order to indicate that the "forward" dissociation and "reverse" recombination processes occur simultaneously during the solvation of a weak electrolyte, an equilibrium arrow, "$$\rightleftharpoons$$," is incorporated into the solution equation for this type of solute.
Because a solution equation is the symbolic representation of a physical change, the chemical formulas, not the chemical names, of the substances that are being transformed and created are incorporated into the pattern that is shown above. Since a solution equation is used to represent the electrolyte behavior of the chemical that is being dissolved, the chemical formula of the solute is written on the left side of the "reaction" arrow. A solution also contains a solvent, which does not undergo a physical change during the dissolving process and, therefore, does not exhibit any electrolyte behavior. As a result, the formula of the solvent should not be written on the left side of the "reaction" arrow. Instead, the chemical formula of the solvent is written over the "reaction" arrow, in order to indicate the presence of this substance in the resultant solution. Because a weak electrolyte partially dissociates, or separates, into its constituent cations and anions as it dissolves, an ion symbol, which indicates the charge of the ion as a superscript on the corresponding elemental symbol, for each of these particles is written on the right side of the "reaction" arrow. Since both cations and anions, which can be monoatomic or polyatomic, are generated during the solvation process, a plus sign, "+", is used to separate their ion symbols.
As stated in Section 7.2, solutions can be prepared using solvents and solutes that exist in the solid, liquid, or gaseous states of matter. If water is utilized to dissolve a solute, the substances that are present in the resultant solution are classified as aqueous, by definition. While these states of matter can be incorporated into a solution equation using the abbreviations "$$\left( s \right)$$," "$$\left( l \right)$$," "$$\left( g \right)$$," and "$$\left( aq \right)$$," respectively, the information that is conveyed by these symbols is not vital to understanding the electrolyte behavior of the solute and, therefore, the states of matter are often omitted from solution equations.
Finally, most solution equations require the incorporation of one or more balancing coefficients, in order to indicate that the Law of Conservation of Matter, which mandates that particles cannot be created or destroyed during a physical or chemical change, is upheld during the solvation process. Recall that a coefficient is a whole-number value that specifies the quantity in which the corresponding particle participates in the transformation that is occurring, and that values of "1" are usually implicitly-understood in chemistry and, therefore, are not written when balancing an equation. As stated above, the solvent does not undergo a physical change during the dissolving process and, consequently, does not exhibit any electrolyte behavior. Therefore, because coefficients are only associated with chemicals that are changing, the chemical formula of the solvent is not considered when balancing a solution equation.
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## 1 Commutative diagram in $\TeX$ revisited
### 1.1 xypic and xyJax
To my knowledge, the only way to type commutative diagram on the web is to use xyJax, a third-party extension of MathJax that render diagram using xypic. This is also how Stacks Project was set up.
The syntax of xypic is almost the same as tikz-cd, to a basic user the only difference is how arrows are typed. I learn xypic syntax by rewriting a GUI editor for tikzcd by Yichuan Shen to output xypic code. Here is the xypic version of the editor. I also host a copy of the tikz-cd editor here.
The configuration of xyJax or any third-party extension MathJax was not very easy for me, since it seems that MathJax CDN no longer hosts third-party extensions. So I have to host my own copy of xyJax and tell MathJax CDN to use it, as indicated in its documentation. Also, one also has to reconfig a path in xyJax.
To config MathJax in org-mode, apropos org-html-mathjax-template.
## 2 LaTeX in Inkscape: Incompatibility between ghostscript and pstoedit<2018-03-30 Fri>
Since Ghostscript 9.22, certain flags (e.g. dREALLYDEALYBIND) are deprecated and pstoedit, a piece of software that Inkscape uses to render LaTeX, remains unchanged since 2005. This makes Inkscape users unable use LaTeX. Textext developers claims that they will switch to pdf2svg frontend in their version 0.8 to avoid this trouble with pstoedit. Meanwhile, the only solution seems to be downgrade ghostscript to 9.21 each time one uses Inkscape. In ArchLinux, one can downgrade a package using pacman:
ls /var/cache/pacman/pkg/ | grep ghostscript
pacman -U /var/cache/pacman/pkg/package-old_version.pkg.tar.xz
or a AUR package called downgrade
I had good experience with both of them (pacman to downgrade php to be compatible with nextcloud, and downgrade for ghostscript)
The problem is well documented here and here.
## 3 LaTeX indentation in org-mode <2018-02-20 Tue>
I was told, in accordance with my experience, that we visually process text better if each line in a paragraph is approximately below 80 characters. This fact is also omnipresent on the internet, standardized tests, books, etc.. being among the fundamentals of web design (except wikipedia, that's why I use Wikiwand).
In Emacs, the key binding M-q will execute the fill-paragraph function that automatically shrinks text and insert "soft" newlines to shorten line below a certain threshold. This function however does not respect the LaTeX structure, e.g. it inserts line break inside inline equation and merge display equation. format paragraph.
This is a long long long long long long long long long paragraph with equation $1+1 = 2+0=3-1=4-2$ with an equation in display $1+ 1 = 2$.
The problem has been noticed around the Internet here and there.
Meanwhile AucTeX does not have this annoying problem. It turns out that AUCTeX maps the M-q key to a different function, called LaTeX-fill-paragraph. So the temporary fix is to load latex.el in org-mode and maps M-q to LaTeX-fill-paragraph
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# RF power amplifier
Not to be confused with Audio power amplifier.
An RF power amplifier
Class C VHF power amplifier based on the transistor MRF317.
A radio frequency power amplifier (RF power amplifier) is a type of electronic amplifier that converts a low-power radio-frequency signal into a higher power signal. Typically, RF power amplifiers drive the antenna of a transmitter. Design goals often include gain, power output, bandwidth, power efficiency, linearity (low signal compression at rated output), input and output impedance matching, and heat dissipation.
Many modern RF amplifiers operate in different modes, called classes, to help achieve their design goals. Some classes are class A, class B, class C and class E.[1] Class D amplifiers are rarely used for RF purposes because they need even higher frequency devices.
Modern RF power amplifiers use solid-state devices such as bipolar junction transistors and MOSFETs.[2] Although transistors and other modern solid-state devices have replaced vacuum tubes in most electronic devices, tubes are still used in some high-power transmitters (see Valve RF amplifier).
## Applications
The basic applications of the RF power amplifier include driving to another high power source, driving a transmitting antenna and exciting microwave cavity resonators. Among these applications, driving transmitter antennas is most well known. The transmitter–receivers are used not only for voice and data communication but also for weather sensing (in the form of a radar).[citation needed]
## Wideband amplifier design
Impedance transformations over large bandwidth are difficult to realize, thus most wideband amplifiers use 50 Ω output loading. Transistor output power is then limited to
${\displaystyle P_{out}\leq {\frac {(V_{br}-V_{k})^{2}}{8Z_{o}}}}$
${\displaystyle V_{br}}$ is defined as the breakdown voltage
${\displaystyle V_{k}}$ is defined as the knee voltage
and typically ${\displaystyle Z_{o}=50\Omega \,}$
The loadline method is often used in RF power amplifier design.[3]
## References
1. ^ Cloutier, Stephen R. "Class E AM Transmitter Descriptions, Circuits, Etc.". www.classeradio.com. WA1QIX. Retrieved 6 June 2015.
2. ^ MFJ Enterprises. "Ameritron ALS-1300 1200-watt NO TUNE TMOS-FET AMPLIFIER" (PDF). MFJ Enterprises. Retrieved 6 June 2015.
3. ^ Matthew Ozalas (January 14, 2015). "How to Design an RF Power Amplifier: The Basics". youtube.com. Retrieved 2015-02-10.
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# Graph g(x)=5^(x+3)
g(x)=5x+3
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y=0.
Horizontal Asymptote: y=0
Graph g(x)=5^(x+3)
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# How to find volatility of Asset given volatility of Stock in Merton model?
I encounter a problem in one of my project to find the 1 year, 2 year and 3 year Asset volatility. We are given 2015 Bell Canada's financial report and a software to do this. The financial report can be found here http://www.bce.ca/investors/financialperformance/annual where asset=47993M, liability=30664M equity=17329M, stock volatility= 15%
According to my lecture notes, we should do the following steps:
1. input data from the financial report into software to find Delta for 1,3,5 year(bottom left section), assuming no dividend
2. using the formula σSS =σVV*(∂S/∂V), plug in value of delta into ∂S/∂V and find σV for 1, 3, 5 year.
However, I do not know what data I should put into the software. In the lecture, I see my prof first uses # of share outstanding* share price=S(equity), and use equity debt ratio to find B(debt) then he put V=B+S(total asset) into the section 'stock price', the given stock volatility into 'volatility', Ke^(rt) (the future debt) into 'exercise price'. Then he compute delta.
I don't quite understand why he did this. Can anyone explain to me what kind of data I should use(market value of equity/book value of equity, market value of asset/book value of asset, market value of debt/book value of debt)? I am really confused.
Thank you very much.
• What software is this? I'm in APM466 too. Also do we have to take into account current assets and liabilities or is just assets and liabilities ok? (Current = 1 year) – RYR Apr 8 '16 at 21:39
• www-2.rotman.utoronto.ca/~hull/software I think we are asked to use this software to find out asset volatility given stock volatility – usagi drop Apr 8 '16 at 22:13
• This is what I did: enter stock price as assets, enter strike price as debt, enter time to expiry as 1/3/5, Risk free rate as Treasury rate, 0 dividends. Then, test different values of Volatility until the value you entered equals the value of 0.15*S/V * delta. That value is the implied asset volatility – RYR Apr 8 '16 at 22:44
## 1 Answer
The delta of an option is the amount the option value will change according to the change in the underlying.
The Book value of a company is typically it's assets minus liabilities. This can differ from market value (which is the share price * number of shares outstanding).
The picture you provided looks like an option calculator, with inputs:
Stock price, Volatility, Risk Free Rate, and Dividends (top left)
Option details - time to expiry, strike, call/put (middle left)
and outputs of option price, Greeks, and a graph on the right.
Edit: I realise now you mean Merton model (credit risk), so...
"Equity can be viewed as a European call option on the firm's assets"... and as inputs we need "current value of the company’s assets, the volatility of the company’s assets, the outstanding debt and the debt maturity."
Basically from this paper:
Let E = value of the firm's Equity, and A = value of assets, and D be debt. Then $E_T = max[A_T – D, 0]$ and we can view equity as a call option on the assets of the firm with strike price equal to the promised debt payment...
I think this summary will be of most help to you...
"$V(0) = D(0) + E(0)$" - as your professor did. Adding equity and debt to get the firm's asset value.
• I think in Merton model, we treat the corporate like an underlying asset, the exercise price = Book value of debt*e^(rt), which is the future debt payment, and option price= Market value of equity. That is all I know. Our purpose is to find Delta using the software, which is the derivative of equity W.R.T asset. The point I got confused is that my prof inputed market value of corporate into the 'stock price' but I don' t know why. Beside, I don't know how to find the market value of asset as well :( – usagi drop Apr 8 '16 at 22:33
• Updated.. I didn't study this, sorry, but I hope the link is helpful to your understanding. – Steinwolfe Apr 9 '16 at 3:19
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# list-manipulation's questions - English 1answer
4.851 list-manipulation questions.
### 1 Efficient way to make updates in a big List
I would like to know is there is a way to do this: ...
### 3 Efficient way to detect peak value changes in a list
3 answers, 122 views list-manipulation peak-detection
ListPlot[list, Joined -> True, PlotRange -> Full]I would like a simple method to get the positions within the list where the values deviate a lot from ...
### 12 Element-wise test on List elements
6 answers, 1.035 views list-manipulation map operators
This question could sound pretty silly but I can't find a way to apply element -wise tests to a list. For example if I digit ...
### 1 Randomly merge elements from paired lists to a new paired list
Some background. I can use Mathematica to generate text book problems/exercises and corresponding answer in two "pairs/synched" lists $L_{Q}$ and $L_{A}$ (i.e. element 1 in each list is a Q&A pair,...
### 2 Subtracting off background data from my data sets
2 answers, 55 views list-manipulation matrix
I don't know how to subtract off background data Data0 from my data sets collected in Datagen. ...
### 4 Change matrix elements at specific locations?
Let's say I have an arraya={{1,2,3}, {4,5,6}, {7,8,9}}I want to have all elements along the diagonal multiplied by 2. ...
### 3 How to assign a list to a desired position of an array?
3 answers, 94 views list-manipulation matrix
This question is related to this. Consider an array array as array = ImageData[RandomImage[10, 10]];And the indices of the ...
### 6 Put an array in a matrix
3 answers, 273 views list-manipulation matrix
Assume that I have a function that generates an $m \times n$ array of numbers and I want to put this array in a specified place in an $(m+n) \times (m+n)$ matrix. How can I do that?
### 1 ListLinePlot of a 3D function, over one of the arguments, with a range of values for the other 2 arguments
1 answers, 38 views plotting list-manipulation table
I have a function of 3 argumentsmu[kx_, ky_, lambda_] := -(kx^2 + ky^2) - (kx^2*(kx^2 + 5*ky^2)*lambda)/(kx^2 + ky^2)^4I want to plot ...
### 2 Optimisation of a loop
I've opened a question here, which was answered. The code works totally fine for a small set of data. However, for a large set and over many iterations, it will take a long time (in order of 24 hours)....
### How to correct not precise values
1 answers, 37 views list-manipulation import precision
I have the source file file = "test.txt" with these values: ...
### 1 Iterative loop for a given list
1 answers, 37 views list-manipulation functions do for
Suppose I have the following list: ...
### 1 Issue with the use of Position
2 answers, 63 views list-manipulation functions
Reading the documentation of Position, I found there's a possible issue:Position looks for matches based on patterns, which may ...
### 5 Subtract lists' elements
I have 2 lists, that have the following form:List1 = {{0.0, val10}, {0.1, val11}, {0.2, val12},...} List2 = {{0.0, val20}, {0.1, val21}, {0.2, val22},...}I ...
### Summing coefficients of multinomial
1 answers, 52 views list-manipulation data
I have data of following form. data = {{1, multi1(z1, z2,..)},{2, multi2(z1, z2,..)},...} I want to add up all the coefficients of corresponding multinomial (and also want to perform different ...
### 7 Deleting list elements by comparing to another list
4 answers, 241 views list-manipulation filtering
I have two lists as follow. The first isp={{"j","d","x"},{"d","k","z"}}and the second one is: ...
### 17 Ordering function with recognition of duplicates
1 answers, 345 views list-manipulation sorting
Fairly often I have a need to get the Ordering of an expression but with recognition of duplicates. For example: ...
### 6 Put edges of a matrix to zero
I have to set the first and last rows and columns to zero rows and columns. I tried with the first column: ...
### 2 labeling data in a list
1 answers, 60 views plotting list-manipulation labeling
I have the following list: l={{1,2},{3,4},{5,6}}I want to list plot above such that the first element {1,2} can be labeled "a", {3,4} labeled "b" and {5,6} to ...
### Identical expressions subtracted from each other giving small but significant errors
0 answers, 29 views list-manipulation precision
In my current code, I have formed a list of numbers with two different methods. For the first method, I wrote ...
### Creating a plot using data imported from Excel
2 answers, 147 views plotting list-manipulation excel
I am trying to create plots starting from values that I have in an Excel spreadsheet. The values of interest are contained in three rows, which I will call 1, 2, and 3 for the sake of this discourse. ...
### 3 Replace non-zero elements with symbol
I have a very large matrix (tensor) in Mathematica with some zero and non-zero elements. I am interested in replacing the non-zero elements with some symbol or a 1 so that it is easier to view the ...
### 7 Nonzero element positions of a matrix
3 answers, 273 views list-manipulation matrix sparse-arrays
Let m={{1, 2, 0}, {4, 0, 9}};I want to find the position of every nonzero element of the above matrix. The code ...
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# Dust properties and star formation of approximately a thousand local galaxies
* Corresponding author
Abstract : Aims. We derived the dust properties for 753 local galaxies and examine how these relate to some of their physical properties. We present the derived dust emission properties, including model spectral energy distribution (SEDs), star formation rates (SFRs) and stellar masses, as well as their relations. Methods. We modelled the global dust-SEDs for 753 galaxies, treated statistically as an ensemble within a hierarchical Bayesian dust-SED modelling approach, so as to derive their infrared (IR) emission properties. To create the observed dust-SEDs, we used a multi-wavelength set of observations, ranging from near-IR to far-IR-to-submillimeter wavelengths. The model-derived properties are the dust masses ($M_{dust}$), the average interstellar radiation field intensities ($U_{av}$), the mass fraction of very small dust grains (“QPAH” fraction), as well as their standard deviations. In addition, we used mid-IR observations to derive SFR and stellar masses, quantities independent of the dust-SED modelling. Results. We derive distribution functions of the properties for the galaxy ensemble and as a function of galaxy type. The mean value of $M_{dust}$ for the early-type galaxies (ETGs) is lower than that for the late-type and irregular galaxies (LTGs and Irs, respectively), despite ETGs and LTGs having stellar masses spanning across the whole range observed. The $U_{av}$ and “QPAH” fraction show no difference among different galaxy types. When fixing $U_{av}$ to the Galactic value, the derived “QPAH” fraction varies across the Galactic value (0.071). The specific SFR increases with galaxy type, while this is not the case for the dust-specific SFR (SFR/$M_{dust}$), showing an almost constant star formation efficiency per galaxy type. The galaxy sample is characterised by a tight relationship between the dust mass and the stellar mass for the LTGs and Irs, while ETGs scatter around this relation and tend towards smaller dust masses. While the relation indicates that $M_{dust}$ may fundamentally be linked to $M_\star$, metallicity and $U_{av}$ are the second parameter driving the scatter, which we investigate in a forthcoming work. We used the extended Kennicutt–Schmidt (KS) law to estimate the gas mass and the gas-to-dust mass ratio (GDR). The gas mass derived from the extended KS law is on average $\sim$20% higher than that derived from the KS law, and a large standard deviation indicates the importance of the average star formation present to regulate star formation and gas supply. The average GDR for the LTGs and Irs is 370, and including the ETGs gives an average of 550.
Keywords :
Domain :
Cited literature [86 references]
https://hal-cea.archives-ouvertes.fr/cea-02319402
Contributor : Edp Sciences <>
Submitted on : Thursday, October 17, 2019 - 9:42:38 PM
Last modification on : Monday, February 10, 2020 - 6:12:39 PM
### File
aa34553-18.pdf
Publication funded by an institution
### Citation
S. Lianou, P. Barmby, A. A. Mosenkov, M. Lehnert, O. Karczewski. Dust properties and star formation of approximately a thousand local galaxies. Astronomy and Astrophysics - A&A, EDP Sciences, 2019, 631, pp.A38. ⟨10.1051/0004-6361/201834553⟩. ⟨cea-02319402⟩
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# MCQs on Filters and Attenuators
## MCQs on Filters and Attenuators
MCQs on Filters and Attenuators, Objective Questions on Filters and Attenuators, MCQs on Filters, MCQs on Attenuators, Filters MCQ, Attenuators MCQ, Gate Questions on Filters, Gate Questions on Attenuators
### Objective Type Questions
1. A 26 dB output in watts is equal to
• 2.4 w
• 0.26 w
• 0.156 w
• 0.4 w
2. The characteristic impedance of an LPF in attenuation band is
• Purely imaginary
• Zero
• Complex frequency
• Real value
3. The real part of the propagation constant shows:
• Variation of voltage and current on basic unit
• Variation of phase shift/position of voltage
• Reduction in voltage, current value of signal amplitude.
• Reduction of only voltage amplitude.
Answer: Reduction in voltage, current value of signal amplitude.
4. The purpose of an attenuator is to
• Increase signal strength
• Decrease reflections
• Decrease value of signal strength
• Provide impedance matching
Answer: Decrease value of signal strength
5. In a transmission line terminated by characteristic impedance, Z0
• There is no reflection of the incident wave
• The reflection is maximum due to termination.
• There are a large number of maximum and minimum on the line.
• The incident current is zero for any applied signal.
Answer: There is no reflection of the incident wave
6. An attenuator is a
• Resistive network
• R-L network
• R-C network
• L-C network.
7. If ‘α’ attenuation in nepers, then
• Attenuation in $dB=\frac{\alpha }{0.8686}$
• Attenuation in dB = 8.686α
• Attenuation in dB = 0.1α
• Attenuation is dB = 0.01α
Answer: Attenuation in dB = 8.686α
8. For a constant K-type high-pass π-Section filter, characteristic impedance Z0 for f < fc is
• Resistance
• Inductive
• Capacitive
• Inductive or capacitive
9. An ideal filter should have
• Zero attenuation in the pass band
• Zero attenuation in the attenuation band
• Infinite attenuation in the pass band
• Infinite attenuation in the attenuation band.
Answer: Zero attenuation in the pass band
10. For an m-derived HPF, the cut-off frequency is 4 kHz and the filter has an infinite attenuation at 3.6 kHz, the value of m is
• 0.436
• 4.36
• 0.34
• 0.6
11. If ZOC = 120 Ω and ZSC = 30 Ω, the characteristic impedance is
• 30 Ω
• 60 Ω
• 120 Ω
• 150 Ω
12. If ZOC = 100 Ω and ZSC = 64 Ω, the characteristic impedance is
• 400 Ω
• 60 Ω
• 80 Ω
• 170 Ω
13. The frequency of infinite attenuation (f) of a low-pass m-derived section is
• Equal to fc
• f = ∞
• Close to but greater than fc
• Close to but less than fc of the filter
Answer: Close to but greater than fc
14. A constant K-type BPF has pass band from 1000 Hz to 4000 Hz. The resonance frequency of shunt and series arm is a
• 2500 Hz
• 500 Hz
• 2000 Hz
• 3000 Hz
15. A constant K-type low-pass T-section filter has Z0 = 600 Ω at zero frequency. At f=fc, the characteristic impedance is
• 600 Ω
• 0 Ω
• ∞ Ω
• more than 600 Ω
16. In m-derived terminating half section, m is equal to
• 0.1
• 0.3
• 0.6
• 0.9
17. In a symmetrical T-type attenuator with attenuation N and characteristic impedance R0, the resistance of each series arm is equal to
• R0
• (N − 1) R0
• $\frac{2N}{N^{2}-1}R_{0}$
• $\frac{N}{N^{2}-1}R_{0}$
Answer: $\frac{2N}{N^{2}-1}R_{0}$
18. For a transmission line, open-circuit and short-circuit impedance are 20Ω and 5 Ω. The characteristic impedance of the line is
• 10 Ω
• 20 Ω
• 25 Ω
• 100 Ω
19. For a prototype LPF, the phase constant β in the attenuation band is
• α
• 0
• $\frac{\pi }{2}$
20. In the m-derived HPF, the resonant frequency is to be chosen so that it is
• Above the cut-off frequency
• Below the cut-off frequency
• Equal to the cut-off frequency
• Infinitely high
21. In a symmetrical π-section attenuator with attenuation N and characteristic impedance R0, the resistance of each shunt arm is equal to
• R0
• (N − 1) R0
• $\frac{N-1}{N+1}R_{0}$
• $\frac{N+1}{N-1}R_{0}$
Answer: $\frac{N+1}{N-1}R_{0}$
22. Bridged T-type network can be used as
• Attenuator
• LPF
• HPF
• BPF
23. One neper is equal to
• 0.8686 dB
• 8.686 dB
• 0.115 dB
• 86.86 dB
24. Terminating half sections used in composite filters are built with the following value of m
• 0.3
• 0.8
• 0.1
• 0.6
25. A transmission line works as
• Attenuator
• LPF
• HPF
• None of these
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Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!
# Find the equation of a line parallel to x-axis and passing through the origin.
Question:
Find the equation of a line parallel to x-axis and passing through the origin.
Solution:
The line parallel to x-axis and passing through the origin is x-axis itself.
Let A be a point on x-axis. Therefore, the coordinates of A are given by (a, 0, 0), where a ∈ R.
Direction ratios of OA are (a − 0) = a, 0, 0
The equation of OA is given by,
$\frac{x-0}{a}=\frac{y-0}{0}=\frac{z-0}{0}$
$\Rightarrow \frac{x}{1}=\frac{y}{0}=\frac{z}{0}=a$
Thus, the equation of line parallel to x-axis and passing through origin is
$\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$
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## What has 'intrinsic value'?
Next
• 72
Needless to add, this subject matter - as complex and convoluted as it can get - is to me very intimately associated with ethics and intrinsic value in general.
That is where it ends up, I think. Happiness, unhappiness and everything you can think of that fit into these (which is everything in experience, for even the plainest most uneventful conditions are saturated with affect. Boredom, perhaps, but that changes nothing) is the existential presupposition for ethics. I cannot even imagine ethics with without some pain or pleasure, or mood, or interest, even, in play, at risk. One cannot, yet, have a moral relation with AI, a dog or cat or squirrel, yes.
But you know, we cannot speak of happiness analytically (Wittgenstein would not), which is a very peculiar thing. We can talk about what makes a person happy or un, but happiness simpliciter is hands off. Can we call this an intrinsic good (or bad)?
• 1.5k
But you know, we cannot speak of happiness analytically (Wittgenstein would not), which is a very peculiar thing. We can talk about what makes a person happy or un, but happiness simpliciter is hands off.
I've been contemplating that a lot lately and for some time now: an idea regarding volitional valence. In short, when we obtain what we intend as intended, volitional happiness (as in the archaic notion of luckiness, good fortune), irrespective of how minor or major the intent. Likewise, when our intention is in any way impeded, volitional suffering (bearing the weight of an unwanted circumstance). All this however is contingent on the reality of intentions and, hence, some notion of teleology - and, in an indirect way, on the reality of freely willed choices. Things of course get very complex, but that's the short version of it. Anyway, addressed because I at least believe it might be possible to speak of happiness analytically in a suitable enough manner, this at least for the topic of ethics.
Curious to hear your thoughts or rebuttables concerning this overall idea.
• 72
Singularity doesn’t step out of plurality, but the other way around. There is no such thing as a centered structure. A play of signifiers is a differential structure with no center.
“Henceforth, it was necessary to begin thinking that there was no center, that the center could not be thought in the form of a present-being, that the center had no natural site, that it was not a fixed locus but a function, a sort of non-locus in which an infinite number of sign-substitutions came into play. This was the moment when language invaded the universal problematic, the moment when, in the absence of a center or origin, everything became discourse-provided we can agree on this word-that is to say, a system in which the central signified, the original or transcendental signified, is never absolutely present outside a system of differences.”(Sign, Structure and Play, Writing and Difference p352)
This system of differences must be thought as a temporal process rather than a simultaneous whole. The system unfolds itself from one singular to the next. Each singular is determinate ( even though it never repeats itself) but not decidable , since it borrows from another element in order to be what it is. It is a double structure. You are right to at there is no determinability in the sense of an ability to retrieve and hold onto an exact same entity or meaning. Determinability for Derrida at the level of social structures is a relative stability of thematic meaning.
I was thinking of an ontological indeterminacy. I mean, if I deconstruct my cat, and the arbitrariness of the signifier cannot be made non arbitrary independently of a context, then the context is the ontological foundation for what my cat is. But beyond this, there is nowhere to go. It is blind metaphysics to think that there can be conceived something beyond context.
This doesn't just annihilate metaphysics, it places annihilated metaphysics in the language construction itself, if I may put it that way. I mean to say, the utterance qua utterance is entirely foreign to the actuality that is in the palpable "fabric of things" and I talk like this notwithstanding Heidegger's claim that objects in the world are "of a piece" with the language used to conceive of them.
You won't agree, I suspect, but I claim there is something irreducible to this actuality. I am not convinced our understanding is locked within a totality of the Same. Yes, I suppose this is walking on water talk.
• 1.2k
What has intrinsic value?
$ART$
• 139
I express my apologies for bothering you, but I hope that you received the message that I sent you. I am a newcomer here, so I do not know exactly this forum works. I hope you have a fantabulous day!
• 2.5k
if I deconstruct my cat, and the arbitrariness of the signifier cannot be made non arbitrary independently of a context, then the context is the ontological foundation for what my cat is.
The signifier-signified relation is never arbitrary for Derrida, s there never is a sign diver by itself, but I understand where you’re going.
I am not convinced our understanding is locked within a totality of the Same.
I assume you’re getting this from Levinas. I respect the Levinasian-Kierkegaardian way of thinking, but I think Levinas misreads Heidegger and Husserl when he accuses them of totalizing phenomenology.
• 72
Curious to hear your thoughts or rebuttables concerning this overall idea.
My thoughts are a work in progress. In play is the indefeasibility of affectivity (this being a general term for a classification of existentials like pleasure, joy, bliss, happiness, disgust, hatred, revulsion, misery, and on and on. I take facts to be Wittgesntein's facts: sailboats are sailing in the distance, or an ox is stronger than a chihuahua. There is nothing of affectivity in all of these. Facts are accidental, that is, they could have been otherwise and there is nothing that makes them necessary. This is on edge of talk about possible worlds, worlds of logical necessity, or worlds of causal boundaries. I take Wittgenstein to be talking about logically conceivable worlds, and in them, there is no affectivity. You could say there is the fact that I am unhappy or ecstatic, but, and here is the rub, as a fact, there is no "good" in happiness., and there is no "bad" in misery. This opens the discussion for an extraordinary exposition the nature of ethics and aesthetics. How is it that I cannot assail the integrity of the, well, "value of value" that is the good of enjoyment the bad of a toothache, in any conceivable arrangements of context? In all possible worlds of factuality, what is good in this analysis of the good has no place at all. And this is because affectivity of goodness is an absolute. It does not issue from a factual matrix, that is, talk about this kind of thing is beyond the deferential possibilities of any context driven ontology.
I have to work this idea out, though I have another life beyond reading and thinking philosophy and likely will never do this entirely. But you see the intuition (heh, if there is such a thing) of this is bound up with this "discovery" (again, is there such a thing? Rorty says truth is made not discovered. Oh my!) of what is in an ethical analysis: There is something, some "invisible X" that cannot be reduced to contextual inter-deferentiality (I made that term up. It seems to be okay), I mean, produced out of "difference" of the meanings of ideas. Ethics and aesthetics are, and the limb I am going out on here is a long and slim one, utterly metaphysical in their very mysterious analysis of foundational ...errr, properties. They issue forth an injunction: Don't do this; Do this.
Of course, ethical injunctions are language constructs, and the same that is true for facts of the world are true here, that is, there is nothing of affect in an injunction, and injunctions are NOT indefeasible. ut this is not about ethics. This is about an abstraction form ethics that reveals an absolute.
Derrida is maddening to read (for me) but when one catches on (such as I have) , one sees how massively interesting he is, especially vis a vis Wittgenstein's Ethics and Tractatus. I mean, this is literally life changing, if, though, one is that caught up in the enterprise if finding out what it is to be a human being at the level of basic questions.
• 2.5k
In play is the indefeasibility of affectivity (this being a general term for a classification of existentials like pleasure, joy, bliss, happiness, disgust, hatred, revulsion, misery, and on and on. I take facts to be Wittgesntein's facts: sailboats are sailing in the distance, or an ox is stronger than a chihuahua. There is nothing of affectivity in all of these. Facts are accidental, that is, they could have been otherwise and there is nothing that makes them necessary. This is on edge of talk about possible worlds, worlds of logical necessity, or worlds of causal boundaries. I take Wittgenstein to be talking about logically conceivable worlds, and in them, there is no affectivity
My central interest since college has been the relationship between affectivity, feeling, mood and emotional on the one hand, and cognition, intentionality and understanding on the other. My view is that the two phenomena are utterly inseparable, that there is no expereince that is without affective valence and quality. I would argue that the sense of a world for Wittgenstein, as use context, is that way in which the word matters to us , its significance and relevance. That is an affective feature. There are no facts without relevance, there is no relevance without value, so understanding a fact is already an affective process.
• 72
My central interest since college has been the relationship between affectivity, feeling, mood and emotional on the one hand, and cognition, intentionality and understanding on the other. My view is that the two phenomena are utterly inseparable, that there is no expereince that is without affective valence and quality. I would argue that the sense of a world for Wittgenstein, as use context, is that way in which the word matters to us , its significance and relevance. That is an affective feature. There are no facts without relevance, there is no relevance without value, so understanding a fact is already an affective process.
I don't see how this can be disagreed with. Experience is not a thing of discreet parts; rather, parts are in the analysis. There is no pure reason and there is no sublime affectivity qua affectivity as some kind of stand alone features of existence. But a question like, what is experience? has to have in its answer something about affectivity and its features, and one feature I find impossibly there is that affect cannot be "defeated" as to what it is by contextual changes. It is what it is regardless of context. And even if this pain can be recast as pleasure (in the mind of a masochist, say) it is not that pain is pleasure, or that pain is therefore made ambiguous, but that it is no longer pain.
BUT: An utterance places pain in context, that is, when I think about pain, I am already in a system of predelineated understandings, and so, what is said is bound to contingency, bound to a foundational deconstruction (as I am calling it. I don't have the vocabulary quite ready to hand) that denies all "stand alone" claims (call them "Platonic" claims). And so, the utterance "pain is bad" is just as contingent as "snow is white". The point I would make is the injunction not to do X is grounded in existence in a way that cannot be spoken, but is "mysteriously authoritative." I think Wittgenstein would agree.
I see that the color red, e.g., is there, but is "speechless" apart from its contextual placement possibilities. Affect "speaks" an inaudible and uninscribable "language" of existence.
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How are the rates of consumption of energy and economic growth connected?
32 views
How are the rates of consumption of energy and economic growth connected?
by (15.5k points)
selected
The rate of consumption of energy is crucial for economic growth or development process of a nation. The consumption of renewable sources of energy is related to sustainable economic development. The renewable sources of energy are free from pollution and health hazard.
Also, energy consumption is essential for promoting agriculture and industrial process. Hence, more use of renewable source of energy leads to more sustained economic development.
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# User:Jan A. Sanders/An Introduction to Leibniz Algebra Cohomology/Lecture 8
## The trace and Killing form
Let $$R$$ be $$\mathbb{C}$$ and $$\dim_\mathbb{C}\mathfrak{a}<\infty\ .$$ Then define $$K_\mathfrak{a}\in C^2(\mathfrak{g},\mathbb{C})$$ by $K_\mathfrak{a}(x,y)=\mathrm{tr}(d_+^{(0)}(x) d_+^{(0)}(y))$ In the case $$\mathfrak{a}=\mathfrak{g}$$ and $$d_+^{(0)}=\mathrm{ad}_+\ ,$$ this is called the Killing form. In general, one calls $$K_\mathfrak{a}$$ the trace form.
### example
Let $$\mathfrak{g}=\mathfrak{sl}_2$$ and $$\mathfrak{a}=\R^2\ ,$$ with the standard representation (see Lecture 1). Then $K_{\R^2}(M,M)=0, \quad K_{\R^2}(M,N)=1,\quad K_{\R^2}(M,H)=0,$ $K_{\R^2}(N,M)=1, \quad K_{\R^2}(N,N)=0,\quad K_{\R^2}(N,H)=0,$ $K_{\R^2}(H,M)=0, \quad K_{\R^2}(H,N)=0,\quad K_{\R^2}(H,H)=2.$
### proposition
$$K_\mathfrak{a}$$ is symmetric.
### proof
This follows from $$\mathrm{tr}(AB)=\mathrm{tr}(BA)$$.$$\square$$
### proposition
$$K_\mathfrak{a}$$ is $$\mathfrak{g}$$-invariant, that is, $$K_\mathfrak{a}\in C^2(\mathfrak{g},\mathbb{C})^\mathfrak{g}\ .$$
### proof
Given the trivial action of $$\mathfrak{g}$$ on $$\mathbb{C}\ ,$$ one has $d^{(2)}(x)K_\mathfrak{a}(y,z)=-K_\mathfrak{a}([x,y],z)-K_\mathfrak{a}(y,[x,z])\ :$ $=-\mathrm{tr}(d_+^{(0)}([x,y]) d_+^{(0)}(z))-\mathrm{tr}(d_+^{(0)}(y) d_+^{(0)}([x,z]))\ :$ $=-\mathrm{tr}(d_+^{(0)}(x) d_+^{(0)}(y) d_+^{(0)}(z))+\mathrm{tr}(d_+^{(0)}(y) d_+^{(0)}(x) d_+^{(0)}(z)) -\mathrm{tr}(d_+^{(0)}(y) d_+^{(0)}(x)d_+^{(0)}(z))+\mathrm{tr}(d_+^{(0)}(y) d_+^{(0)}(z)d_+^{(0)}(x))\ :$ $=0$
### proposition
$d^2 K_\mathfrak{a}\in C_{\wedge}^3(\mathfrak{g},\mathbb{C})$
### proof
From the $$\mathfrak{g}$$-invariance it follows that $d^2 K_\mathfrak{a}(x,y,z)=K_\mathfrak{a}(x,[y,z])$ Furthermore, $K_\mathfrak{a}(x,[z,y])=\mathrm{tr}(d_+^{(0)}(x) d_+^{(0)}([z,y]))\ :$ $=-\mathrm{tr}(d_+^{(0)}(x) d_+^{(0)}([y,z]))$ $=-K_\mathfrak{a}(x,[y,z])$ and $K_\mathfrak{a}(z,[x,y])=-K_\mathfrak{a}(z,[y,x])=K_\mathfrak{a}([y,z],x)=K_\mathfrak{a}(x,[y,z])$$$\square$$
### corollary
Let $$\mathfrak{g}$$ be a Lie algebra. Then $[d^2 K_\mathfrak{a}]\in H_{\wedge}^3(\mathfrak{g},\mathbb{C})$ Observe that this class is not trivial, since $$K_\mathfrak{a}$$ is symmetric, not antisymmetric.
### musical maps
Let $$\mathfrak{g}^\star=C^1(\mathfrak{g},\mathbb{C})$$ and define $$\flat: \mathfrak{g}\rightarrow \mathfrak{g}^\star$$ by $\flat(x)(y)=K_\mathfrak{a}(x,y)$
### proposition
$\flat\in Hom_\mathfrak{g}(\mathfrak{g},\mathfrak{g}^\star)$
### proof
$\flat([x,y])(z)=K_\mathfrak{a}([x,y],z)\ :$ $=-K_\mathfrak{a}(y,[x,z])\ :$ $=-\flat(y)([x,z])\ :$ $=d^{(1)}(x)\flat(y)(z)$ or $$\flat([x,y])=d^{(1)}(x)\flat(y)\quad \square\ .$$
Define $\sharp:\mathfrak{g}^\star\rightarrow \mathfrak{g}$ by $K_\mathfrak{a}(\sharp(c^1),y)=c^1(y)$ Then $K_\mathfrak{a}(x,y)=\flat(x)(y)=K_\mathfrak{a}(\sharp(\flat(x)),y)\ ,$ or $$x-\sharp(\flat(x))\in \ker K_\mathfrak{a}\ .$$
### proposition
$$\ker K_\mathfrak{a}$$ is an ideal.
### proof
Let $$y\in\ker K_\mathfrak{a}\ ,$$ that is $$K_\mathfrak{a}(x,y)=0$$ for all $$x\in\mathfrak{g}\ .$$ Then it follows from the invariance of $$K_\mathfrak{a}$$ that $K_\mathfrak{a}([y,x],z)+K_\mathfrak{a}(y,[x,z])=0$ and therefore $$K_\mathfrak{a}([y,x],z)=0$$ for all $$z\in\mathfrak{g}\ .$$ This shows that $$[\mathfrak{g},\ker K_\mathfrak{a}]\subset \ker K_\mathfrak{a}\ .$$ The statement that $$[\ker K_\mathfrak{a},\mathfrak{g}]\subset \ker K_\mathfrak{a}$$ follows by a symmetry argument.
### definition
A Leibniz algebra $$\mathfrak{g}$$ is called simple if $$[\mathfrak{g},\mathfrak{g}]\neq 0$$ and $$\mathfrak{g}$$ contains no ideals besides $$0$$ and itself.
### proposition
If $$\mathfrak{g}$$ is simple, then $$\mathfrak{g}=[\mathfrak{g},\mathfrak{g}]\ .$$
### proof
$$[\mathfrak{g},\mathfrak{g}]\neq 0$$ is an ideal, so it must equal $$[\mathfrak{g},\mathfrak{g}]=\mathfrak{g}\ .$$
### proposition
If $$K_\mathfrak{a}$$ is nonzero, and $$\mathfrak{g}$$ is simple, then $$\flat$$ is injective.
### proof
Let $$x\in\ker\flat\ .$$ Then $$0=\flat(x)(y)=K_\mathfrak{a}(x,y)$$ for all $$y\in\mathfrak{g}\ ,$$ that is, $$x\in \ker K_\mathfrak{a}\ .$$ But $$\ker K_\mathfrak{a}$$ must be zero, so $$x=0\ .$$
### proposition
Let $$\mathfrak{h}$$ be an ideal in $$\mathfrak{g}\ .$$ Define $\mathfrak{h}^\perp=\{x\in\mathfrak{g}|K_\mathfrak{g}(x,y)=0 \quad \forall y\in \mathfrak{h}\}$ Then $$\mathfrak{h}^\perp$$ is an ideal in $$\mathfrak{g}\ .$$
### proof
Let $$g\in\mathfrak{g}\ ,$$ $$h\in\mathfrak{h}$$ and $$k\in\mathfrak{h}^\perp\ .$$ Then $K_\mathfrak{g}([g,k],h)=-K_\mathfrak{g}(k,[g,h])=0$ This shows that $$[\mathfrak{g},\mathfrak{h}^\perp]\subset \mathfrak{h}^\perp$$ and similarly $$[\mathfrak{h}^\perp,\mathfrak{g}]\subset \mathfrak{h}^\perp\ .$$
### definition
One defines a series of ideals of $$\mathfrak{g}\ ,$$ the derived series, as follows. $\mathfrak{g}^{(0)}=\mathfrak{g}$ $\mathfrak{g}^{(i+1)}=[\mathfrak{g}^{(i)},\mathfrak{g}^{(i)}]$ If, for some $$n\in\mathbb{N}\ ,$$ $$\mathfrak{g}^{(n)}=0$$ then $$\mathfrak{g}$$ is called solvable.
### well defined
$$\mathfrak{g}^{(0)}$$ is an ideal in $$\mathfrak{g}\ .$$ Suppose that $$\mathfrak{(i)}$$ is an ideal for $$i=0,\dots,n\ .$$ Then $[\mathfrak{g},\mathfrak{g}^{(n+1)}]=[\mathfrak{g},[\mathfrak{g}^{(n)},\mathfrak{g}^{(n)}]]\ :$ $\subset [[\mathfrak{g},\mathfrak{g}^{(n)}],\mathfrak{g}^{(n)}]+[\mathfrak{g}^{(n)},[\mathfrak{g},\mathfrak{g}^{(n)}]]\ :$ $\subset [\mathfrak{g}^{(n)},\mathfrak{g}^{(n)}]=\mathfrak{g}^{(n+1)}$ The inclusion $$[\mathfrak{g}^{(n+1)},\mathfrak{g}]\subset \mathfrak{g}^{(n+1)}$$ follows in a similar way. By induction it follows that all the $$g^{(i)}$$'s are ideals in $$\mathfrak{g}$$
### corollary
For $$i\leq j \ ,$$ $$\mathfrak{g}^{(j)}$$ is an ideal in $$\mathfrak{g}^{(i)}\ .$$
### remark
If $$\mathfrak{g}$$ is solvable (that is, $$\mathfrak{g}^{(n)}=0$$ for some $$n$$), then it contains an abelian ideal (namely $$\mathfrak{g}^{(n-1)}$$).
### proposition
If $$\mathfrak{g}$$ is solvable, then all its subalgebras and homomorphic images are.
### proof
Let $$\mathfrak{h}$$ be a subalgebra. Then $$\mathfrak{h}^{(0)}\subset\mathfrak{g}^{(0)}\ .$$ Assume $$\mathfrak{h}^{(i)}\subset\mathfrak{g}^{(i)}\ .$$ Then $\mathfrak{h}^{(i+1)}=[\mathfrak{h}^{(i)},\mathfrak{h}^{(i)}]\subset [\mathfrak{g}^{(i)},\mathfrak{g}^{(i)}]=\mathfrak{g}^{(i+1)}$ and the statement is proved by induction. Similarly, let $$\phi:\mathfrak{g}\rightarrow \mathfrak{h}$$ be surjective, and assume $$\phi:\mathfrak{g}^{(i)}\rightarrow \mathfrak{h}^{(i)}$$ to be surjective. Then $\phi(\mathfrak{g}^{(i+1)})=\phi([\mathfrak{g}^{(i)},\mathfrak{g}^{(i)}])=[\phi(\mathfrak{g}^{(i)}),\phi(\mathfrak{g}^{(i)})]= [\mathfrak{h}^{(i)},\mathfrak{h}^{(i)}]=\mathfrak{h}^{(i+1)}$
### proposition
If $$\mathfrak{h}$$ is a solvable ideal such that $$\mathfrak{g}/\mathfrak{h}$$ is solvable, then $$\mathfrak{g}$$ is solvable.
### proof
Say $$(\mathfrak{g}/\mathfrak{h})^{(n)}=0\ .$$ Let $$\pi:\mathfrak{g}\rightarrow \mathfrak{g}/\mathfrak{h}$$ be the canonical projection. Then $$\pi(\mathfrak{g}^{(n)})=(\mathfrak{g}/\mathfrak{h})^{(n)}=0$$ or $$\mathfrak{g}^{(n)}\subset \mathfrak{h}\ .$$ Since $$\mathfrak{h}^{(m)}=0\ ,$$ $$\mathfrak{g}^{(n+m)}=(\mathfrak{g}^{(n)})^{(m)}\subset \mathfrak{h}^{(m)}=0\ ,$$ implying the statement.
### proposition
If $$\mathfrak{h}, \mathfrak{k}$$ are solvable ideals of $$\mathfrak{g}\ ,$$ then so is $$\mathfrak{h}+\mathfrak{k}\ .$$
### proof
One has $(\mathfrak{h}+ \mathfrak{k})/\mathfrak{k}\equiv \mathfrak{h}/(\mathfrak{h}\cap \mathfrak{k})$ Since $$\mathfrak{h}$$ is solvable, so is $$\mathfrak{h}/(\mathfrak{h}\cap \mathfrak{k}) \ .$$ But this implies that $$\mathfrak{h}+\mathfrak{k}\ ,$$ since $$\mathfrak{k}$$ is solvable.
### propostion
If $$\dim \mathfrak{g}<\infty\ ,$$ there exists a unique maximal solvable ideal in $$\mathfrak{g}\ ,$$ the radical of $$\mathfrak{g}\ ,$$ denoted by $$\mathrm{Rad\ }\mathfrak{g}\ .$$
### proof
Let $$\mathfrak{s}$$ be a maximal solvable ideal in $$\mathfrak{g}\ .$$ Suppose $$\mathfrak{h}$$ is another solvable ideal. Then $$\mathfrak{s}+\mathfrak{h}\supset \mathfrak{s}$$ is solvable, and by the maximality, $$\mathfrak{s}+\mathfrak{h}= \mathfrak{s}\ ,$$ that is, $$\mathfrak{h}\subset\mathfrak{s}\ .$$
### definition
A Leibniz algebra $$\mathfrak{g}$$ is called semisimple if $$\mathrm{Rad\ }\mathfrak{g}=0\ .$$
### proposition
If $$\mathfrak{g}$$ is simple, it is semisimple
### proof
For a simple Leibniz algebra the derived series is stationary, that is, $$\mathfrak{g}^{(i)}=\mathfrak{g}$$ for all $$i\in\mathbb{N}\ .$$ The only other possible ideal is $$0\ ,$$ so this must be $$\mathrm{Rad\ }\mathfrak{g}\ .$$
### proposition
$$\mathfrak{g}/\mathrm{Rad\ }\mathfrak{g}$$ is semisimple.
### proof
Let $$[\mathfrak{h}]$$ be a nonzero solvable ideal in $$\mathfrak{g}/\mathrm{Rad\ }\mathfrak{g}\ .$$ Then $$\mathfrak{h}+\mathrm{Rad\ }\mathfrak{g}$$ strictly contains $$\mathrm{Rad\ }\mathfrak{g}\ ,$$ which is in contradiction with its maximality. Thus $$\mathfrak{h}\subset \mathrm{Rad\ }\mathfrak{g}\ ,$$ that is, $$[\mathfrak{h}]$$ is the zero ideal in $$\mathfrak{g}/\mathrm{Rad\ }\mathfrak{g}\ .$$
### proposition
If $$\ker K_\mathfrak{g}=0\ ,$$ then $$\mathfrak{g}$$ is semisimple.
### proof
Let $$\mathfrak{h}$$ be an abelian ideal of $$\mathfrak{g}\ .$$ Take $$h\in\mathfrak{h}, g\in\mathfrak{g}\ .$$ Then $$ad_+(h)ad_+(g)$$ maps $$\mathfrak{g}$$ to $$\mathfrak{h}\ .$$ Thus $$(ad_+(h)ad_+(g))^2=0\ .$$ This implies that $K_\mathfrak{g}(h,g)=\mathrm{tr}(ad_+(h)ad_+(g))=0$ In other words, $$\mathfrak{h}\subset\ker K_\mathfrak{g}=0\ .$$ If there are no abelian ideals, then there are no solvable ideals besides $$0\ ,$$ that is, $$\mathfrak{g}$$ is semisimple.
### theorem
Let $$\mathfrak{g}$$ be a solvable subalgebra of $$\mathfrak{gl}(\mathfrak{a})\ ,$$ $$\dim\mathfrak{a}<\infty\ .$$ If $$\mathfrak{a}\neq 0\ ,$$ then $$\mathfrak{a}$$ contains a common eigenvector for all endomorphisms in $$\mathfrak{g}\ .$$
### proof
Induction on $$\dim\mathfrak{g}\ .$$ Since $$\mathfrak{g}$$ is solvable, it properly contains $$\mathfrak{g}^{(1)}=[\mathfrak{g},\mathfrak{g}]\ ,$$ otherwise $$\mathfrak{g}^{(i)}=\mathfrak{g}$$ for $$i\in\mathbb{N}\ .$$ Since $$\mathfrak{g}/[\mathfrak{g},\mathfrak{g}]$$ is abelian, subspaces are ideals. Take a subspace of codimension one. Then the inverse image $$\mathfrak{h}$$ in $$\mathfrak{g}$$ is an ideal of codimension one which includes $$[\mathfrak{g},\mathfrak{g}]\ .$$ $$\mathfrak{h}$$ is solvable, and by the induction assumption there exists a vector $$a\in\mathfrak{a}$$ such that $$a$$ is an eigenvector for each $$h\in\mathfrak{h}\ ,$$ that is, $h a=\lambda(h)a,\quad\lambda\in C^1(\mathfrak{h},\mathbb{C})$ (the exceptional case here is when $$\dim \mathfrak{h}=0\ .$$ In that case, $$\mathfrak{g}$$ onedimensional and abelian, so one takes an eigenvector of a generator of $$\mathfrak{g}$$). Let $\mathcal{W}=\{a\in\mathfrak{a}|x a=\lambda(x)a \quad \forall x\in \mathfrak{h}\}$ Now for $$x\in\mathfrak{g}$$ and $$y\in\mathfrak{h}$$ one finds $y x w=x y w-[x,y] w=\lambda(y) x w-\lambda([x,y])w\ .$ If one can prove that $$\lambda([x,y])=0$$ then $$\mathcal{W}$$ is invariant under the action of $$\mathfrak{g}\ .$$
Fix $$x\in \mathfrak{g}\ ,$$ $$w\in\mathcal{W}\ .$$ Let $$n>0$$ be the smallest integer such that $$w, xw, \dots, x^n w$$ are linearly dependent. Let $$\mathcal{W}_0=0$$ and $$\mathcal{W}_i$$ be the subspace of $$\mathfrak{a}$$ spanned by $$w, xw,\dots, x^{i-1} w\ .$$ It follows that $$\dim\mathcal{W}_n=n$$ and $$W_{n+i}=W_n, i\geq 0\ .$$ Each $$\mathcal{W}_i$$ is invariant under $$y\in\mathfrak{h}\ .$$ The matrix of $$y$$ is upper triangular with eigenvalue $$\lambda(y)$$ on the diagonal. This implies $$\mathrm{tr}_{\mathcal{W}_i}(y)=i\lambda(y)\ .$$ Since $$[x,y]\in\mathfrak{h}\ ,$$ one also has $\mathrm{tr}_{\mathcal{W}_n}([x,y])=i\lambda([x,y])$ Both $$x$$ and $$y$$ leave $$\mathcal{W}_n$$ invariant, so the trace of $$[x,y]$$ must be zero. Thus $$n\lambda([x,y])=0\ .$$ This shows that $$\mathcal{W}$$ is invariant under the action of $$\mathfrak{g}\ .$$
Write $$\mathfrak{g}=\mathfrak{h}+\mathbb{C} z\ .$$ Let $$w_0 \in\mathcal{W}$$ be an eigenvector of $$z$$ (acting on $$\mathcal{W}$$). Then $$w_0$$ is a common eigenvector of $$\mathfrak{g}\ .$$
### definition (flag)
Let $$\mathfrak{a}$$ be a finite dimensional vectorspace ($$\dim\mathfrak{a}=n$$). A flag is a chain of subspaces $0=\mathfrak{a}_0\subset\mathfrak{a}_1\subset\dots\subset\mathfrak{a}_n=\mathfrak{a},\quad \dim\mathfrak{a}_i=i$ If $$x\in\mathrm{End}(\mathfrak{a})\ ,$$ one says that $$x$$ leaves the flag invariant if $$x \mathfrak{a}_i\subset \mathfrak{a}_i$$ for $$i=1,\dots,n\ .$$
### theorem (Lie)
Let $$\mathfrak{g}$$ be a solvable subalgebra of $$\mathfrak{gl}(\mathfrak{a}), \dim\mathfrak{a}=n<\infty\ .$$ Then $$\mathfrak{g}$$ leaves a flag in $$\mathfrak{a}$$ invariant.
### proof
It follows from the proof above that there exists a codimension one $$\mathfrak{g}$$-invariant subspace. Let that be $$\mathfrak{a}_{n-1}\ .$$ Repeat the argument starting with $$\mathfrak{a}_{n-1}$$ instead of $$\mathfrak{a}_{n}$$ and use induction.
### lemma
Let $$\mathfrak{g}$$ be solvable. Then there exists a flag of ideals $0=\mathfrak{g}_0\subset\mathfrak{g}_1\subset\dots\subset\mathfrak{g}_n=\mathfrak{g},\quad \dim\mathfrak{g}_i=i$
### proof
Let $$d_+^{(0)}:\mathfrak{g}\rightarrow \mathfrak{gl}(\mathfrak{a})$$ be a finite dimensional representation of $$\mathfrak{g}\ .$$ Then $$d_+^{(0)}(\mathfrak{g})$$ is solvable, and stabilizes a flag in $$\mathfrak{a}\ .$$ Take $$\mathfrak{a}=\mathfrak{g}$$ and $$d_+^{(0)}=\mathrm{ad}_+\ ,$$ then the $$\mathfrak{g}_i$$ are ideals (since they are $$\mathfrak{g}$$-invariant) and they obey the flag condition.
### lemma
Let $$\mathfrak{g}$$ be solvable. Then $$x\in\mathfrak{g}^{(1)}$$ implies that $$\mathrm{ad}_\mathfrak{g}(x)$$ is nilpotent.
### proof
From the flag of ideals construct a basis. relative to this basis the matrix of $$\mathrm{ad}_\mathfrak{g}(y), y\in \mathfrak{g}\ ,$$ is upper triangular. Thus the matrix of $$\mathrm{ad}_\mathfrak{g}(x), x\in \mathfrak{g}^{(1)}$$ is strictly upper triangular, and therefore nilpotent.
### remark
In the next lecture it is shown that this implies that $$\mathfrak{g}^{(1)}$$ is nilpotent (to be defined).
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# Market capitalisation
A measure of the total value of a company’s outstanding shares according to the stock market, market capitalisation is often referred to simply as ‘market cap’ or ‘capitalised value’. Market capitalisation is used by investors to classify companies into large-cap, mid-cap or small-cap, which is frequently used as an investment criterion, particularly when trying to maintain diversification in a portfolio of assets.
As with most investor ratios, market cap is often used in conjunction with other measures – such as book value – to help analyse a company’s overall value to the shareholder.
### How is it calculated?
Calculating market cap is simple and uses the formula:
The price per share of a company and the number of outstanding shares can usually be found out either from newspapers or the internet. The audited accounts will always give the outstanding or issued share capital. A company’s market cap should always be quoted in the currency unit in which the shares are priced.
### Example
Company JKL’s shares are quoted at \$3.46 each. The company has 3,500,000 shares outstanding. Using the above formula, the company’s market capitalisation is \$12,110,000 (\$3.46 x 3,500,000) which according to the classifications below would make it a small-cap company.
### Classifications
Classifications are arbitrary but will typically be:
##### Large-cap:
In excess of \$10 billion or perhaps \$5 billion
##### Mid-cap:
\$2 billion to \$10 billion or \$1 billion to \$5 billion
##### Small-cap:
Less than \$2 billion or less than \$1 billion
### Free-float market capitalisation
The above method for calculating market capitalisation is referred to as the full market capitalisation. In reality however, not all of the outstanding shares are freely available to be traded – they may be ‘locked’ in a government or strategic holding for example. This information can usually be found out from the company itself or the exchange. There may also be more than one class of share.
Free-float market capitalisation is calculated by multiplying the full market cap by what is known as the free-float factor. This is determined by dividing the number of shares readily available for trading in the market by the total number of shares outstanding, and rounding it up or down to the nearest 0.05 increment.
If we continue with the example of company JKL and if, out of the 3,500,000 shares outstanding, 2,875,000 are readily available to trade, the company’s free-float factor can be calculated as 0.8, calculated as follows:
This means that the company’s free-float market capitalisation is $12,110,000×0.8=9,688,000$.
### Considerations
Market capitalisation will fluctuate on a daily basis as price per share is based on the value assigned to the shares by the stock market. This also means that as a measure, market cap is largely opinion based – depending on a company’s reputation in the market.
This therefore means that market capitalisation might not necessarily be a true measure of a company’s underlying value. That is why the measure is used alongside other measures and ratios when evaluating a company’s financial value.
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Vim has a built-in scripting language. It’s what you write your vimrc in, and it’s really convenient for short one-off tasks.
It sucks otherwise.
I’ll focus on just one reason: its Boolean string comparisons are so bad as to be actively misleading. You should never use them.
• == depends on user case-sensitivity settings. So if you’ve set ignorecase, == is case-insensitive. You need to append # and ? to every comparison operator to get case-sensitive or insensitive comparisons.
• If a string is compared with a number, the entire string is cast to a number by looking for leading digits, using them as the number to cast to, and dropping the rest of the string. If no number can be formed this way, it’s cast to 0. Meaning 0 will always have a truthy comparison with any string that doesn’t start with numbers.
These are all true comparisons (the " is vim’s comment character. Another mistake, considering that " is also a string delimiter.)
" ignorecase is on
'a' == 'A'
'abc' == 'AbC'
0 == 'nonemptystring'
0 == ''
0 == '0f'
0 == '000000f'
1 == '01f'
1 == '01f'
These are all false.
0 == '0'
You have to use is? and is# to get proper comparisons. If you want something like python’s == for values that aren’t lists/dicts/containers, use is#. For containers, == seems to actually work properly.
Syntax is supposed to be a trade-off between terseness and readability. Vim’s comparison operators achieve neither.
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# Algorithm to calculate dispersion and effective index in mode solution
#1
Hello,
I like to know, how Mode solution calculate the group velocity dispersion? Is it a fit? What is the algorithm to do it?
I also like to know, what is the algorithm in Mode solution to calculate “effective index”.
Thanks,
#2
FDE uses Maxwell’s equations to solve the eigenvalue problem for a given geometry and boundary condition at a specific frequency/wavelength. Details of the work can be found in the link below:
https://kb.lumerical.com/solvers_feem.html
After solving the equations, the effective index can be calculated from $n_{eff}=c_0\beta/\omega$.
To calculate the group index or dispersion, you need to enable “detailed dispersion calculation” in the Frequency analysis tab. Solver then will shift $\omega = \omega+\delta\omega$ and will calculate new $\beta$ values to calculate $d\omega/d\beta$.
The link below might be useful to view as well:
Group Velocity Dispersion Calculation in MODE Solutions
For the completeness of this thread, you can also calculate the phase and group velocity from field vectors (from “Optical Waveguide Theory” by Allan Synder and John Love, page 230, table 11-1):
$v_p = \omega/\beta=\frac{1}{\mu_0}\frac{\int n^2|E|^2dA}{\int n^2E\times H^*\cdot\hat{z}dA}$
$v_g = d\omega/d\beta=\frac{1}{\epsilon_0}\frac{\int E\times H^*\cdot\hat{z}dA}{\int n^2|E|^2dA}$
Where integrals are calculated over the entire simulation region.
#3
Thanks @bkhanaliloo.
It does make sense.
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News: IT'S THE 2ND ANNUAL GUATEMALA LIBRARY PROJECT BOOK DRIVE! LOOKING FOR DONATIONS OF SCIENCE BOOKS THIS YEAR. Check it out in the "Extending the Hand of Kindness" folder or here: http://www.etiquettehell.com/smf/index.php?topic=139832.msg3372084#msg3372084
• January 18, 2017, 09:09:27 AM
### Author Topic: Your holiday hill to die on. (Read 675577 times)
0 Members and 2 Guests are viewing this topic.
#### PastryGoddess
• Member
• Posts: 7416
##### Re: Your holiday hill to die on.
« Reply #1305 on: February 15, 2014, 11:51:12 PM »
I bought 30 boxes of chocolate for $1 for each of the companies and staff I'm managing. I'm still trying to come up with a witty name for Feb 18th when they'll get it Bloody Mary Day. That would be Queen Mary Tudor, daughter of Henry VII and Katharine of Aragon. It's her birthday. (Also DD2's -- she was MOST miffed when she found out who shared her birthday!) Ooooh I was thinking of inviting everyone to Sunday brunch next week (Restaurant Week) Bloody Mary Day would fit in nicely. Maryland #### Lorelei_Evil • Member • Posts: 2312 ##### Re: Your holiday hill to die on. « Reply #1306 on: February 16, 2014, 12:40:50 AM » I thought of you all at Godiva today... #### PastryGoddess • Member • Posts: 7416 ##### Re: Your holiday hill to die on. « Reply #1307 on: February 16, 2014, 03:40:38 PM » I may have visited walmart and picked up some more chocolate...allegedly Maryland #### MummySweet • Member • Posts: 662 ##### Re: Your holiday hill to die on. « Reply #1308 on: February 16, 2014, 03:54:43 PM » I bought 30 boxes of chocolate for$1 for each of the companies and staff I'm managing.
I'm still trying to come up with a witty name for Feb 18th when they'll get it
Bloody Mary Day. That would be Queen Mary Tudor, daughter of Henry VIII and Katharine of Aragon. It's her birthday.
(Also DD2's -- she was MOST miffed when she found out who shared her birthday!)
Edited because I really do know which English king married Katharine of Aragon!
It's John Travolta's, Molly Ringwald's, Matt Dillon's, Yoko Ono's and Dr. Dre's birthday too. Maybe one of those would be better for your DD? (It's mine too, but I doubt she would get too excited about that... )
#### GlitterIsMyDrug
• Member
• Posts: 1120
##### Re: Your holiday hill to die on.
« Reply #1309 on: February 18, 2014, 04:04:06 PM »
I love this idea, and will steal it for next year!
Our Valentines went over very well! Partner and BFF's husband joined us and we visited with a lot of the residents, it was really awesome. The husband handed one gentleman a card and the man sat him down and told him how ever year his wife would make him a Valentine's card, they were high school sweethearts and she'd started it in high school and continued every year, but she passed away 4 years ago and he hadn't had a valentine card since because people don't think guys like valentines, and long story short he made the husband start tearing up. Partner and I got tons of questions about the wedding, how long we'd been together, how we met, the proposal story, and BFF and husband were fielding plenty of similar questions of their own. It was so fun. I full recommend stealing the idea.
In other news, the trip to see great uncle went very well. He's in good spirits and was tickled to see us. He gave us valentines and chocolates and flowers because "Every nice girl deserves flowers'. Got to play with my new cousin (great-uncle's son's daughter), then we um...well we got married. Not on V-day actually, but on Saturday. We got the license and whatnot on Friday, then had a very tiny wedding in my great uncle's backyard, officiated by a friend of ours who happens to live over there. We were just gonna do the court house deal (we'd have to do it later anyways, not legal in our state), but great uncle wouldn't hear of it, he wanted to see us married the right way! So we threw together an incredibly quick wedding. We'll still have our "real" wedding next year, but now the legal stuff is out of the way!
It'd been Partner's plan all along, so that my great-uncle could see me get married (since we aren't sure he'll still be with us next year), and she clued me in the morning we were leaving. She'd gotten her siblings to meet us out there with her mom, and my two best friends as well, my mom was already coming and my grandparents were already out there. Honestly, it was perfect. And we went out to eat at this Jewish deli afterwards, we had the brisket.
#### daen
• Member
• Posts: 1332
##### Re: Your holiday hill to die on.
« Reply #1310 on: February 18, 2014, 04:17:00 PM »
Oh, Glitter, congrats! I'm laughing and tearing up at the same time!
Wishing you and Partner all the best, forever.
#### Tabby Uprising
• Member
• Posts: 451
##### Re: Your holiday hill to die on.
« Reply #1311 on: February 18, 2014, 04:27:31 PM »
Oh my goodness, Glitter! Congratulations! Got some nonrhythmic happy dancing going on for you!
#### PastryGoddess
• Member
• Posts: 7416
##### Re: Your holiday hill to die on.
« Reply #1312 on: February 18, 2014, 04:30:56 PM »
Congrats Glitter!
Maryland
• Member
• Posts: 13346
• Not all those who wander are lost
##### Re: Your holiday hill to die on.
« Reply #1313 on: February 18, 2014, 05:37:00 PM »
I am so happy right now! And the brisket!
“All that is gold does not glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost."
-J.R.R Tolkien
#### GlitterIsMyDrug
• Member
• Posts: 1120
##### Re: Your holiday hill to die on.
« Reply #1314 on: February 18, 2014, 05:42:44 PM »
I am so happy right now! And the brisket!
It was really funny actually because we roll in and the waitress comes over and tells us they have a brisket dinner special (we were there at like 4pm, it was empty other then us) and everyone at the table busts up laughing and my grandfathers both go "We'll have the brisket". Then we had to tell the very sweet waitress the whole story, plus the we just got married story.
#### jayhawk
• Member
• Posts: 1372
##### Re: Your holiday hill to die on.
« Reply #1315 on: February 18, 2014, 08:06:57 PM »
Best wishes, Glitter! So happy for you.
#### gramma dishes
• Member
• Posts: 9542
##### Re: Your holiday hill to die on.
« Reply #1316 on: February 18, 2014, 08:09:14 PM »
Yes, this Valentine's weekend was definitely one you'll remember all your life! What a sweet story. And of course, congratulations and best wishes!!
#### GratefulMaria
• Member
• Posts: 776
##### Re: Your holiday hill to die on.
« Reply #1317 on: February 18, 2014, 09:01:00 PM »
Aww, congratulations Glitter!
#### crella
• Member
• Posts: 1356
##### Re: Your holiday hill to die on.
« Reply #1318 on: February 18, 2014, 09:16:17 PM »
Congratulations!
#### jedikaiti
• Swiss Army Nerd
• Member
• Posts: 3688
• A pie in the hand is worth two in the mail.
##### Re: Your holiday hill to die on.
« Reply #1319 on: February 18, 2014, 10:28:59 PM »
CONGRATS!!!
What part of v_e = \sqrt{\frac{2GM}{r}} don't you understand? It's only rocket science!
"The problem with re-examining your brilliant ideas is that more often than not, you discover they are the intellectual equivalent of saying, 'Hold my beer and watch this!'" - Cindy Couture
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## Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory
##### Authors
Geng, L. S.
Camalich, J. Martin
Alvarez-Ruso, L.
Vacas, M. J. Vicente
##### Description
We calculate the baryon magnetic moments using covariant Chiral Perturbation Theory ($\chi$PT) within the Extended-on-mass-shell (EOMS) renormalization scheme. By fitting the two available low-energy constants (LECs), we improve the Coleman-Glashow description of the data when we include the leading SU(3) breaking effects coming from the lowest-order loops. This success is in dramatic contrast with previous attempts at the same order using Heavy Baryon (HB) $\chi$PT and covariant Infrared (IR) $\chi$PT. We also analyze the source of this improvement with particular attention on the comparison between the covariant results.
Comment: 4 pages, 2 figures, accepted for publication in PRL
##### Keywords
High Energy Physics - Phenomenology
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Pulse electric fish evaluate successive electrosensory images generated by self-emitted electric discharges, creating a neural representation of the physical world. Intervals between discharges (system resolution) are controlled by a pacemaker nucleus under the influence of reafferent signals. Novel sensory stimuli cause transient accelerations of the pacemaker rate(novelty responses). This study describes quantitatively the effect of changes in contrast of reafferent electrosensory signals on the amplitude and probability of novelty responses. We found that: (i) alterations of a single image in an otherwise homogeneous series cause a novelty response; (ii) the amplitude of the elicited novelty response is a linear function of the logarithm of the change in image contrast; (iii) the parameters of this function, threshold and proportionality constant, allowed us to evaluate the transference function between change in stimulus amplitude and the amplitude of the novelty response; (iv) both parameters are independent of the baseline contrast; (v) the proportionality constant increases with the moving average of the contrast of hundreds of previous images. These findings suggest that the electrosensory system (i) calculates the difference between each reafferent electrosensory image and a neural representation of the past electrosensory input (template'); (ii) creates the comparison template in which the relative contribution of every image decreases with the incorporation of successive images. We conclude that contrast discrimination in the electrosensory system of G. carapo obeys the general principle of appreciating any instantaneous input by the input's departure from a moving average of past images.
Pulse-discharging, weakly electric fish actively electrolocate by emitting electric organ discharges and sensing changes provided by objects on transepidermal self-generated electric fields. In this way they create a series of discrete electric images on a cutaneous electroreceptive mosaic(Lissmann, 1958; cf. Bullock, 1986, 1999; Bastian, 1986). In this study we examine how fish discriminate between electrosensory images of different contrast. This kind of analysis requires unambiguous definition and measurement of the stimulus (input) and of the related performance of a sensory system (output; Marr,1982). Our recent knowledge of electric image generation mechanisms allowed us to control and measure the electrosensory image(Caputi and Budelli, 1995; Rasnow, 1996; Caputi et al., 1998; Stoddard et al., 1999; Nelson and MacIver, 1999; Budelli and Caputi, 2000; Sicardi et al., 2000; Caputi et al., 2003). Whereas the input is a clearly defined physical entity, the output of a sensory system can be considered as a broad spectrum of intangible facts'. Although sensation and perception may exist independently of any behavioural response,only behaviour can be measured objectively(Spector, 2000). So, we restricted our research to the analysis of an orienting behavior (a specific behavioural act directed towards the extraction of information from the environment'; Sokolov,1990) elicited by changes in stimulus contrast, aiming to infer electrosensory processing mechanisms.
Pulse gymnotids show a typical orienting behavior, the novelty response(Lissmann, 1958; Szabo and Fessard, 1965; Larimer and McDonald, 1968; Bullock, 1969; cf. Hopkins, 1983; Kramer, 1990; Moller, 1995). This behavior consists of a transient shortening of the inter-electric organ discharge (EOD)interval triggered by changes in nearby impedance. It has been frequently used to test a fish's electrolocation ability and to assess the effects of reafferent and exafferent input on pacemaker frequency(Bullock, 1969; Heiligenberg, 1980; Grau and Bastian, 1986; Hall et al., 1995; Zellick and von der Emde,1995; Post and von der Emde,1999).
After studying novelty responses evoked by a short-circuit in the presence of different amounts of noise, Heiligenberg(1980) inferred that B. occidentalis develop and maintain a template' or central register of past electroreceptive afferences against which novel afferent input is compared'. Taking into account this hypothesis we posed the following questions: what information is extracted from the input? What information is stored in the comparison template'? What are the rules relating changes in electrosensory image and electromotor output?
Our experiments showed that: (i) the system compares the contrast of every input image with a moving average of the contrast of past images, (ii) when contrast difference between the actual input and the moving average of past images overcomes a threshold, a novelty response is evoked, and (iii) the amplitude of the novelty response is graded with the contrast difference.
Non-sexually differentiated Gymnotus carapo L., a South American pulse-emitting, weakly electric fish, 12-25 cm in length, were used in this study. Fish were gathered in the Laguna del Sauce, Uruguay, under the regulations of the Ministry of Ganadería y Agricultura. All experiments conformed with the rules of the Committee for Use of Experimental Animals of the Instituto de Investigaciones Biológicas Clemente Estable, and the guidelines of the Society for Neuroscience and the International Guiding Principles for Biomedical Research Involving Animals.
### Experimental set up
Fish were held in a net in the middle of a tank (18 cm×25 cm×10 cm) containing 3 liters of water with a conductivity of 100±10 μS cm-1. To create and change an electric stimulus-object' we used a method introduced by von der Emde(1990). A cylindrical stimulus-object (2 mm diameter, 1 cm length) was oriented with its long axis perpendicular to the skin of the electrosensory fovea(Castelló et al.,2000). The two ends of the cylinder were made of graphite carbon discs (1.5 mm in diameter) inserted into a non-conducting plastic tube. The carbon ends were connected to an optocoupled switch (Hamlin HE721 Eneka SA,Montevideo, Uruguay) via insulated copper wires (Cerba SA,Montevideo, Uruguay), which left the tube at its center. To avoid non-controlled stimuli due to the reaction of carbon impurities with water,the probe was maintained immersed in water of 100 μS cm-1conductivity for a few days prior to beginning the experiments until completion. In addition, and for the same purpose, we followed the procedure described by von der Emde(1990) of connecting a large capacitor (2.2 μF) in series with the switch that did not alter the recorded local EOD (LEOD) waveform.
To quantify the local electric image contrast, the voltage drop between the bare tip of a 100 μm diameter insulated copper wire placed against the skin and the base of the stimulus-object cylinder nearest to the fish was measured(Fig. 1A). These electrodes were 2mm apart and thus the electric field in V cm-1 was five times the voltage drop between the electrodes. Signals were amplified (×100),and filtered (band pass 10-10000 Hz, AM Systems, Inc. Carlsborg WA, USA); a digital oscilloscope (Hewlett-Packard model 54601A, USA) was used for observation of individual LEOD waveforms that were also sampled (20 kHz,12-bit resolution, Lab Master DMA A/D card, Scientific Solutions Solon, Ohio,USA) for off-line measurement of the inter-EOD interval (home made signal processing program).
Fig. 1.
Characterization of reafferent electrosensory image and its changes. (A)The diagram illustrates the methodology employed. Local electric organ discharge (LEOD) of Gymnotus carapo was recorded between an electrode adjacent to the skin, and the closest base of a cylindrical object placed 2 mm away from the skin. The electrode was a 100 μm bare-tip insulated wire; the object consisted of a 2 mm diameter, 10 mm long plastic tube with a carbon plug electrode in each opening. An external variable resistor r0 was connected to the carbon plugs to set the baseline amplitude (bPP) of the local EOD. A second variable resistor r1 was periodically connected in parallel, using a timed switch setting the comparison LEOD amplitude (cPP). Changes in object longitudinal resistance resulted in marked changes in image contrast. (B) LEOD recorded at the center of the image of a cylindrical object facing the electrosensory fovea. Left: baseline LEOD obtained without load(r=∞) and right: comparison LEOD obtained when the same object was loaded with a short circuit (r=0). Wave components are labeled as V1, V3 and V4 (according to the nomenclature introduced by Trujillo-Cenóz et al., 1984; V2 is not present at the foveal region). (C)The object resistance change mainly effects the contrast of the image. The amplitudes of each of these LEOD peaks are one-to-one' functions of the peak-to-peak LEOD (PP), indicating that changes in waveform are small and predictable from the change in PP. (D) The electric image of a metal cylinder consists of a Mexican-hat spatial profile. This is illustrated by the plot of the change in the peak of V3 caused by the presence of the object as a function of distance from the projection of the center of the object. The dotted line indicates the amplitude of V3 in the absence of the object (modified from Caputi et al.,2003).
Fig. 1.
Characterization of reafferent electrosensory image and its changes. (A)The diagram illustrates the methodology employed. Local electric organ discharge (LEOD) of Gymnotus carapo was recorded between an electrode adjacent to the skin, and the closest base of a cylindrical object placed 2 mm away from the skin. The electrode was a 100 μm bare-tip insulated wire; the object consisted of a 2 mm diameter, 10 mm long plastic tube with a carbon plug electrode in each opening. An external variable resistor r0 was connected to the carbon plugs to set the baseline amplitude (bPP) of the local EOD. A second variable resistor r1 was periodically connected in parallel, using a timed switch setting the comparison LEOD amplitude (cPP). Changes in object longitudinal resistance resulted in marked changes in image contrast. (B) LEOD recorded at the center of the image of a cylindrical object facing the electrosensory fovea. Left: baseline LEOD obtained without load(r=∞) and right: comparison LEOD obtained when the same object was loaded with a short circuit (r=0). Wave components are labeled as V1, V3 and V4 (according to the nomenclature introduced by Trujillo-Cenóz et al., 1984; V2 is not present at the foveal region). (C)The object resistance change mainly effects the contrast of the image. The amplitudes of each of these LEOD peaks are one-to-one' functions of the peak-to-peak LEOD (PP), indicating that changes in waveform are small and predictable from the change in PP. (D) The electric image of a metal cylinder consists of a Mexican-hat spatial profile. This is illustrated by the plot of the change in the peak of V3 caused by the presence of the object as a function of distance from the projection of the center of the object. The dotted line indicates the amplitude of V3 in the absence of the object (modified from Caputi et al.,2003).
### Experimental design
The experimental design was inspired by the methodology introduced by Weber and formalized by Fechner (cited by Werner, 1980). Weber's procedure was based on what is now known as comparative unidimensional judgements', where a subject is asked to discriminate between two stimuli. A particular stimulus of a given type (baseline or standard stimulus) is applied alternately with one of a number of other stimuli (the comparison stimulus)that are of the same type but differ in a single physical parameter(Werner, 1980).
According to Caputi et al.(1998), Sicardi et al.(2000) and Budelli and Caputi(2000), the electrosensory image of a resistive cylindrical object has a Mexican-hat'-shaped profile,controllable by changing the load resistance, and confirmed by our results obtained in the present study. Thus a single parameter, the amplitude of the signal at the center of the Mexican-hat' profile, can be used to estimate the contrast of the electric image of the stimulus-object.
The experiments were performed at the perioral region, where density,variety and central representation of the sensory mosaic are maximal, and therefore this region has been defined as an electrosensory fovea. At this region, background stimulus in the absence of objects is spatially coherent(i.e. it shows the same triphasic waveform all over the foveal region; Aguilera et al., 2001). At the perioral region, resistive objects modulate the local field, generating aMexican hat' spatial profile of the stimulus amplitude(Fig. 1). Despite this,modulation is associated with small waveform changes, which are predictable from the total energy of the local stimulus(Aguilera and Caputi, 2003; Fig. 1). Therefore, the amplitude pattern is sufficient to describe the image of resistive objects. Since the normalized spatial pattern is not modified when the distance of the object remains constant (Budelli and Caputi, 2000), the change in amplitude at the top of the Mexican hat profile' (i.e. the skin facing the object) describes the change of the image. Consequently, the contrast of the image generated by a resistive stimulus-object can be estimated by a single parameter: the peak-to-peak amplitude (PP) of the local electric field at the skin facing the object.
It should be noted that PP in the presence of the object may be larger or smaller than PP recorded in the absence of the object. When the object load was a resistor of 100 kΩ a flat profile equivalent to that observed in the absence of the object was recorded, and this image has null contrast. Resistors lower than 100 kΩ generated top-external Mexican hat'profiles (Fig. 2A, right) and resistors higher than 100 kΩ generated top-internal Mexican hat'profiles (Fig. 2A, left).
Fig. 2.
Experimental paradigm. (A) The schematic diagrams illustrate the experimental procedures and the corresponding electric images when the change in contrast is maximum (r0=∞ and r1=0). Note the opposite orientation of the Mexican-hat'profile, referred in the text as top-inward' and top-outward', respectively. The raw record at the center of the Mexican hat' allowed us to measure the difference (ΔPP) between the baseline amplitude and comparison amplitude of the stimulus. The temporal course of the corresponding novelty response elicited by the change in object resistance is shown in the bottom plot. (B)Studies were performed using series of trials consisting of a baseline period followed by a comparison period. Four variables were controlled: the baseline amplitude (depending on r0), the comparison amplitude(depending on r1), the number of baseline images(depending on the duration of the baseline period), the number of comparison images (depending on the duration of the comparison period). (C—F) The experimental paradigms used to elucidate the following issues. The number of images different from the baseline that suffice for detection (C); the effect of the difference between baseline and comparison amplitudes (ΔPP) on the amplitude and the probability of the novelty response (D); the effects of the baseline on amplitude and probability of the novelty response (E); and the effect of stimulus history on the amplitude and probability of the novelty response (F).
Fig. 2.
Experimental paradigm. (A) The schematic diagrams illustrate the experimental procedures and the corresponding electric images when the change in contrast is maximum (r0=∞ and r1=0). Note the opposite orientation of the Mexican-hat'profile, referred in the text as top-inward' and top-outward', respectively. The raw record at the center of the Mexican hat' allowed us to measure the difference (ΔPP) between the baseline amplitude and comparison amplitude of the stimulus. The temporal course of the corresponding novelty response elicited by the change in object resistance is shown in the bottom plot. (B)Studies were performed using series of trials consisting of a baseline period followed by a comparison period. Four variables were controlled: the baseline amplitude (depending on r0), the comparison amplitude(depending on r1), the number of baseline images(depending on the duration of the baseline period), the number of comparison images (depending on the duration of the comparison period). (C—F) The experimental paradigms used to elucidate the following issues. The number of images different from the baseline that suffice for detection (C); the effect of the difference between baseline and comparison amplitudes (ΔPP) on the amplitude and the probability of the novelty response (D); the effects of the baseline on amplitude and probability of the novelty response (E); and the effect of stimulus history on the amplitude and probability of the novelty response (F).
Four variables were controlled during the experiments: (i) baseline contrast estimated as PP before a change in the resistance of the object, (ii)baseline duration, (iii) comparison contrasts estimated as PP after a change in the resistance of the object, and (iv) comparison stimulus duration. The difference between baseline contrast and comparison contrast (ΔPP) is referred to as contrast change. As the electromotor activity is a series of brief and discrete events, the changes in duration of either the baseline or the comparison periods lead to changes in the number of images evaluated during these periods.
In order to control these four parameters, the longitudinal resistance of the stimulus-object was changed by means of the optocoupled switch timed with an S88 stimulator (Grass Instruments, Quincy, MA, USA). In each experiment, an external variable resistor r0 was connected between the carbon discs to set the baseline contrast. A second, variable resistor r1 was connected periodically in parallel to shunt r0, and thus set the comparison contrast (Fig. 2).
### Data analysis
Novelty responses are transient reductions of the interval after a change in image contrast. To detect novelty responses, we plotted the peristimulus inter-EOD interval (I) sequence. For each response the intervals were numbered starting at the first interval after the resistance change(I1, I2....In). The baseline inter-EOD interval (I0) was defined as the mean of the 5 intervals preceding the change in stimulus-object resistance and its lower confidence limit as the mean minus 2 standard errors (S.E.M.). Two criteria were employed to define a novelty response: (1) a successive shortening of two intervals immediately after the change in impedance and (2)a second interval (I2) significantly smaller than the baseline confidence limit (I2<I0-2 S.E.M.). The probability of the novelty response for a given experimental condition was estimated as the relative frequency of novelty responses in a set of trials. We defined the amplitude of the novelty response as the normalized maximum shortening of the inter-EOD interval (novelty response amplitude = 1 — minimum of I/I0). The second interval was the briefest in most cases (I3 was exceptionally the briefest).
Stimulus-object resistance (determining PP) was controlled in a trial-to-trial manner, setting independently the number and amplitude of both baseline and comparison stimuli. Our experimental paradigms were designed to answer the following questions.
(1) How many images different from baseline have to occur to be detected?In order to elucidate whether the number of comparison stimuli determine the characteristics of the novelty response, we compared the effects of two stimulation patterns differing only in the duration of the comparison period. Single odd events (in which the contrast of a single image was increased) were compared with increase-and-hold patterns (in which the contrast of approximately 100-120 successive images were increased during a 4 s period). For every change in contrast (ΔPP), two trials were done. In one case the sequence was baseline—increase and hold—baseline—single odd event, and in the other it was baseline—single odd event—baseline—increase and hold. Baseline contrast was constant(r0=∞ open circuit) and baseline duration was 30 s. The results are shown in Fig. 4.
Fig. 4.
Study of the effect of the number of comparison images on the amplitude of the novelty response. (A) The amplitude of the novelty responses elicited by a single odd event (left) and an increase-and-hold pattern (middle) are not significantly different (t-test, P<0.05, N=20). In the right plot, normalized intervals (1-I/I0) obtained using both experimental paradigms are plotted one-to-one, according to their ordinal number. The linear relationship indicates a similar time course for both novelty responses. (B) Amplitude of the novelty response as a function of difference between baseline and comparison amplitudes (ΔPP) obtained applying a single-odd-event pattern (open symbols) and an increase-and-hold pattern (filled symbols). The experimental protocols are illustrated in the inset. Starting from a single baseline level (43 mV cm-1 in the example), each trial consisted of a pair of stimuli: a single odd event followed 30 s later by a 4 s held stimulus of identical ΔPP, or vice versa. In successive trials ΔPP was varied in a random fashion.
Fig. 4.
Study of the effect of the number of comparison images on the amplitude of the novelty response. (A) The amplitude of the novelty responses elicited by a single odd event (left) and an increase-and-hold pattern (middle) are not significantly different (t-test, P<0.05, N=20). In the right plot, normalized intervals (1-I/I0) obtained using both experimental paradigms are plotted one-to-one, according to their ordinal number. The linear relationship indicates a similar time course for both novelty responses. (B) Amplitude of the novelty response as a function of difference between baseline and comparison amplitudes (ΔPP) obtained applying a single-odd-event pattern (open symbols) and an increase-and-hold pattern (filled symbols). The experimental protocols are illustrated in the inset. Starting from a single baseline level (43 mV cm-1 in the example), each trial consisted of a pair of stimuli: a single odd event followed 30 s later by a 4 s held stimulus of identical ΔPP, or vice versa. In successive trials ΔPP was varied in a random fashion.
(2) How different should the comparison image be for detection? In most sensory systems, discrimination depends on baseline level (Weber and Fechner's and Stevens' laws; Werner,1980). In order to study whether the baseline contrast level influence the amplitude of the novelty response, we explored the effects of similar changes in contrast (ΔPPs) starting at different baselines. Increase-and-hold patterns (baseline period, 29 s; comparison period, 1 s)were applied, starting at several different baseline PP values. Up to 30ΔPP values were explored in each fish for every baseline PP (7 fish; the results are shown in Fig. 5A).
Fig. 5.
Probability and amplitude of the novelty response as functions of the increase in image contrast (ΔPP). (A) Amplitude of the novelty response plotted as a function of ΔPP. Data obtained, starting at different baseline contrast, are represented by: 109.27 mV cm-1 (closed circles), 101.35 mV cm-1 (open triangles), 85.43 mV cm-1(open circles), 58.15 mV cm-1 (open squares) and 51.05 mV cm-1 (closed squares). Parameters calculated fitting the data obtained, starting from every baseline contrast, were similar to those from pooled data. Curve-fitting of the pooled data: novelty response amplitude=0.105×log10(ΔPP/5.77), r=0.778, N=216, P<0.0001. (B) Probabilities of evoking novelty responses are plotted as a function of ΔPP. Each point represents the probability of evoking a novelty response estimated by its relative frequency in 10 trials using a given pair of baseline contrast and ΔPP in the same fish. Baseline contrast: 58 mV cm-1 (closed squares), 77 mV cm-1 (open circles), 88 mV cm-1 (closed circles) and 108 mV cm-1 (open squares). The threshold50 (ΔPP yielding novelty responses in 50% of the cases) is indicated by the arrow.
Fig. 5.
Probability and amplitude of the novelty response as functions of the increase in image contrast (ΔPP). (A) Amplitude of the novelty response plotted as a function of ΔPP. Data obtained, starting at different baseline contrast, are represented by: 109.27 mV cm-1 (closed circles), 101.35 mV cm-1 (open triangles), 85.43 mV cm-1(open circles), 58.15 mV cm-1 (open squares) and 51.05 mV cm-1 (closed squares). Parameters calculated fitting the data obtained, starting from every baseline contrast, were similar to those from pooled data. Curve-fitting of the pooled data: novelty response amplitude=0.105×log10(ΔPP/5.77), r=0.778, N=216, P<0.0001. (B) Probabilities of evoking novelty responses are plotted as a function of ΔPP. Each point represents the probability of evoking a novelty response estimated by its relative frequency in 10 trials using a given pair of baseline contrast and ΔPP in the same fish. Baseline contrast: 58 mV cm-1 (closed squares), 77 mV cm-1 (open circles), 88 mV cm-1 (closed circles) and 108 mV cm-1 (open squares). The threshold50 (ΔPP yielding novelty responses in 50% of the cases) is indicated by the arrow.
(3) Is the amplitude of the response graded with the change in image contrast? If so, what is the function that describes the relationship? To explore the effect of the previous electrosensory stimulation on the amplitude of the novelty response, we performed two sets of experiments. In the first set, the relative duration of the baseline and comparison periods were modified from trial to trial, without changing the total trial duration (the results are shown in Fig. 6). In five fish, trial duration was 30 s, and in the other two fish trial duration was 100 s. In all trials, the amplitudes of the baseline and comparison image contrasts were set by stimulus-object resistances of 470 kΩ and 15 Ω, respectively. In the second set of experiments, the duration of baseline period and ΔPP were both varied (three fish; the results are shown in Fig. 7A,B). Three baseline periods and four ΔPP were explored for each fish. In each case the comparison stimulus was set by one of four different r1 values (100 kΩ, 47 kΩ, 22 kΩ or 15 Ω) connected in parallel with r0 (470 kΩ), which also set the baseline contrast. Each trial began with a period in which the stimulus had the same amplitude as the comparison stimulus, followed by a baseline period of the desired duration (2, 10 or 29 s), and ending by a comparison period lasting 1 s. In all cases the trial lasted 30 s.
Fig. 6.
Dynamics of the storage and update of the neural representation of the electric image. Amplitude of the novelty response is plotted as a function of the number of local electric organ discharges (LEODs) in the baseline period. Values are means ± S.D. of the novelty response amplitude(I/I0) obtained in series of trials having baseline periods of the same duration. The inset illustrates the experimental paradigm. The duration of the baseline period of the increase-and-hold pattern was varied to change the number of baseline LEODs before the amplitude step. The number of baseline LEODs were counted (short baseline periods) or estimated by multiplying the period duration by the fish EOD rate. Trial duration was 100 s(two fish, filled symbols) or 30 s (three fish, open symbols). Each symbol shape represents a different fish.
Fig. 6.
Dynamics of the storage and update of the neural representation of the electric image. Amplitude of the novelty response is plotted as a function of the number of local electric organ discharges (LEODs) in the baseline period. Values are means ± S.D. of the novelty response amplitude(I/I0) obtained in series of trials having baseline periods of the same duration. The inset illustrates the experimental paradigm. The duration of the baseline period of the increase-and-hold pattern was varied to change the number of baseline LEODs before the amplitude step. The number of baseline LEODs were counted (short baseline periods) or estimated by multiplying the period duration by the fish EOD rate. Trial duration was 100 s(two fish, filled symbols) or 30 s (three fish, open symbols). Each symbol shape represents a different fish.
Fig. 7.
Parameters of the function relating novelty response and the change in image contrast (ΔPP). (A) Results obtained in a single fish using different increase-and-hold patterns of stimulation, where the amplitude of the novelty response (I/I0) is plotted as a function ofΔPP for three different baseline periods. Symbols indicate the duration of the baseline period: 2 s (open squares; 44 EODs), 10 s (closed circles; 210 EODs), 29 s (open circles; 600 EODs). Trial duration was the same in all experiments (30 s). Note that the scaling constant (the slope of the line fitting the data) increases as a function of the duration of the baseline period. (B) The scaling constants, obtained in the same way in three fish, are plotted as a function of the number of baseline local electric organ discharges (LEODs) (r2=0.88, P<0.01, N=8). Each symbol corresponds to a different fish. (C,D)Threshold50 was studied in three fish for different baseline periods. Probability of evoking novelty responses is plotted as a function ofΔPP. In (C) data obtained from a single fish using baselines of 2 s(closed triangles), 10 s (closed circles) and 29 s (open circles) are compared. In (D) the results were obtained using extreme baseline periods; 0.5 s (open symbols) and 29 s (filled symbols) are compared. Each symbol shape corresponds to a different fish (N=3).
Fig. 7.
Parameters of the function relating novelty response and the change in image contrast (ΔPP). (A) Results obtained in a single fish using different increase-and-hold patterns of stimulation, where the amplitude of the novelty response (I/I0) is plotted as a function ofΔPP for three different baseline periods. Symbols indicate the duration of the baseline period: 2 s (open squares; 44 EODs), 10 s (closed circles; 210 EODs), 29 s (open circles; 600 EODs). Trial duration was the same in all experiments (30 s). Note that the scaling constant (the slope of the line fitting the data) increases as a function of the duration of the baseline period. (B) The scaling constants, obtained in the same way in three fish, are plotted as a function of the number of baseline local electric organ discharges (LEODs) (r2=0.88, P<0.01, N=8). Each symbol corresponds to a different fish. (C,D)Threshold50 was studied in three fish for different baseline periods. Probability of evoking novelty responses is plotted as a function ofΔPP. In (C) data obtained from a single fish using baselines of 2 s(closed triangles), 10 s (closed circles) and 29 s (open circles) are compared. In (D) the results were obtained using extreme baseline periods; 0.5 s (open symbols) and 29 s (filled symbols) are compared. Each symbol shape corresponds to a different fish (N=3).
(4) Does the baseline level have influence on the amplitude or probability of the response? Similar experimental paradigms were used to explore the probability of eliciting novelty responses. The probability of novelty response as a function of ΔPP and baseline PP was studied in five fish. Discrimination experiments consisted of 10-20 cycles in which object resistance was alternated between two values, every 30 s. We never found novelty responses for decreases in the image contrast even though we explored up to the largest possible ΔPP (stepping from short to open circuit, Fig. 3B). Thus, for the purpose of detailed analysis, the low amplitude period was considered as the baseline contrast. Probability distribution curves as a function of ΔPP were constructed for 4-6 baseline contrasts (results shown in Fig. 5B). Threshold50 (T50) was defined as the ΔPP eliciting novelty responses in 50% of the cases.
Fig. 3.
Electromotor responses to changes in contrast of the electrosensory image of a cylindrical object. (A,B) Mean ± S.D. of the normalized intervals(1-I/I0) plotted as a function of the interval order(N=10 trials). (A) The increase of electric image contrast elicits a typical novelty response characterized by a shortening of the first two intervals after the change in image contrast followed by a slow relaxation curve. Note the significant increase in the S.D. (ANOVA, P<0.01).(B) The same change in contrast but in opposite direction does not elicit a novelty response although there is a significant increase of variability(ANOVA, P<0.01). (C) Single trial recordings of the local electric organ discharge (LEOD) illustrating the experimental paradigm.
Fig. 3.
Electromotor responses to changes in contrast of the electrosensory image of a cylindrical object. (A,B) Mean ± S.D. of the normalized intervals(1-I/I0) plotted as a function of the interval order(N=10 trials). (A) The increase of electric image contrast elicits a typical novelty response characterized by a shortening of the first two intervals after the change in image contrast followed by a slow relaxation curve. Note the significant increase in the S.D. (ANOVA, P<0.01).(B) The same change in contrast but in opposite direction does not elicit a novelty response although there is a significant increase of variability(ANOVA, P<0.01). (C) Single trial recordings of the local electric organ discharge (LEOD) illustrating the experimental paradigm.
(5) Finally, does the stimulation history have an influence on the amplitude or probability of the response? In three other fish we applied asymmetric cycles to evaluate the influence of stimulation history on the T50. Cycles consisted of 29, 10, 2 or 0.5 s baseline periods and 1, 20, 28 or 29.5 s comparison periods, respectively, and the results are shown in Fig. 7C,D.
### The novelty response evoked by changes in electric image contrast as a tool to explore electrosensory discrimination
The effective stimulus for each electroreceptor is the local self-generated transepidermal field. This field, in turn, corresponds to the mean current density flowing locally through the skin facing the stimulus-object. It is proportional to the voltage drop between the recording electrodes (called in most previous literature local electric organ discharge', LEOD). It is important to note that G. carapo is a pulse fish that evaluates discrete electric images generated by its own EODs (reafferent electrosensory input) emitted every 20-50 ms. The EOD in fact generates a complex time waveform, whose four components have different origins and distributions along the fish body (V1, V2, V3 and V4,following the nomenclature of Trujillo-Cenóz et al.,1984). In each trial, object resistance was alternated between a baseline and a comparison value, producing marked changes of PP at the skin facing the object. At the snout of G. carapo the skin is densely covered with electroreceptors and has been likened to an electrosensory fovea(Castelló et al.,2000). In this region the field is a collimated and spatially coherent waveform composed of V1, V3 and V4components (Castelló et al.,2000; Aguilera et al.,2001) (Fig. 1A). For different resistive loads, the amplitude of each of these components is unambiguously related to PP (Fig. 1B). Electrosensory images generated by pure resistive cylindrical objects consist of a Mexican-hat' center-surround opposed pattern. Its general shape depends on the object distance and its center-surround difference is scaled monotonically with object conductivity(Caputi et al., 1998; Sicardi et al., 2000; Budelli and Caputi, 2000; see Fig. 1C, modified from Caputi et al., 2003). A large object close to the electric organ should provoke changes of the equivalent load impedance in the surrounding medium and, consequently, in the total current output. However, in our experiments the net change in total current caused by the presence of the probe (stimulus-object) can be considered negligible due to its small size and relative distance from the energy source. Therefore, the stimulus resulting from the presence of our stimulus-object can be considered as a local modulation of the transcutaneous current density pattern without changing the total output current. We altered the stimulation pattern by changing the longitudinal resistance of a cylindrical stimulus-object placed with its axis perpendicular to the skin of the foveal region. Thus, a change in the stimulus-object resistance caused what is operatively defined (by analogy with vision nomenclature) as a change in the contrast of the electric image at the electrosensory fovea. In addition, as mentioned above, the shape of the image of the stimulus-object remained similar whereas its amplitude changed in proportion to the value of PP at its center. Therefore, in our experimental conditions this single parameter, PP at the center of the Mexican-hat' profile, was used to estimate the contrast of the electric image of the object and will be considered in this study as the control stimulus.
A decrease of object impedance (that produced an increase in electrosensory stimulus contrast, Fig. 2B,C)evoked a typical novelty response consisting of an immediate shortening of the next two inter-EOD intervals (Figs 2C,D and 3, left). The third interval after the change in image contrast was usually similar or a little longer than the second. Over the subsequent discharges the inter-EOD intervals slowly returned to the initial baseline values. In addition, the variability of the EOD interval after the change in object resistance was larger than during the baseline period (Fig. 3A). This typical pattern was constant for novelty responses evoked by changes in self-generated electric images, allowing us to distinguish these novelty responses unequivocally from other acceleration-slow return patterns (cf. Moller, 1995).
Interestingly, we found that only the variability of inter-EOD intervals increased in response to a reduction in image contrast; novelty responses were absent (Fig. 3B). Although the observed change in interval variability could indicate image discrimination,its analysis was not included in this study.
Changes in image contrast induced by a change in object impedance were presented with a minimum interval of 30 s. This period included 600-1200 EODs,depending on the baseline pacemaker mean frequency. During successive trials,the amplitude of the novelty response elicited by the same pattern of stimulus varied randomly around a mean value, which indicates that under our experimental conditions the electrosensory-evoked novelty response did not show habituation. This finding is consistent with the observations of Grau and Bastian (1986), who showed the lack of habituation of novelty responses to novel stimuli presented at intervals larger than 20 s.
### A single discrepancy in image contrast is sufficient to provoke the novelty response
Novelty responses, as other types of orienting responses, result from comparing a sensory input with some kind of expectation(Sokolov, 1990). To understand this kind of comparison we investigated firstly how many images constitute the sensory input that is compared with the expectation signals. In other gymnotid fish and under a different stimulation protocol, the amplitude of the novelty response has been reported to increase with the number of images modified by the novel stimuli (Heiligenberg,1980). On the other hand, Bullock(1969) studied the novelty response in a variety of pulse gymnotids and concluded that ... the electroreceptor input has a cycle by cycle access to the pacemaker'. Similar results were obtained in pulse mormyrids by Meyer(1982), suggesting that fish evaluate single images against a stored representation.
Thus, the first set of experiments were designed to test the hypothesis that a sustained increase in contrast of various subsequent reafferent images is more efficient for provoking novelty responses than an increase in the contrast of a single reafferent image.
In three fish a series of 10 novelty responses resulting from a maximum increase in contrast of a single image (single odd event) were compared with a series of 10 novelty responses resulting from a maximum increase in contrast of several consecutive images (increase-and-hold pattern). For the same experimental conditions, the mean amplitude of the novelty response evoked by a single odd event was larger in some fish and smaller in others than the mean amplitude responses evoked by an increase-and-hold pattern. Statistical analysis performed for each of the fish showed no significant differences between the means (t-test, P<0.01). Fig. 4A shows an example from one fish comparing the effects of both stimulus patterns. The mean amplitude of the novelty responses to a single odd event was larger but not statistically significant (t-test, P<0.01, N=10)than the mean amplitude of the novelty responses to a increase-and-hold pattern. The similarity in the relaxation time course of both novelty responses is illustrated by the linear relationship when one response is plotted against the other (Fig. 4A, right); the slope of the line depends on the occasional difference between mean amplitudes. From these experiments it can be seen that, irrespective of the subsequent duration of the comparison period, the initial increase in contrast of the image (ΔPP) not only triggers the novelty response but also determines its amplitude. Once the response is triggered, it follows a time course that is not controlled by the subsequent electrosensory input.
The amplitude of the novelty response was graded according to the evoked increment in the image contrast, following the same relationship independently of the number of comparison stimuli (Fig. 4B). Responses to the increase-and-hold pattern were compared with those evoked by single odd event following the protocols illustrated in the inset. Starting from a single baseline level (r0=∞),each trial consisted of a pair of stimuli: a single odd event followed 30 s later by a 4 s held stimulus of identical ΔPP, or vice versa. In successive trials ΔPP was varied randomly. We observed that the amplitude of the novelty response increased similarly with ΔPP for both stimulation patterns. The amplitude of the novelty response was well fitted by a logarithmic function of ΔPP:
$\ \mathrm{Novelty\ response\ amplitude}=\mathrm{K}{\times}\mathrm{log}_{10}({\Delta}\mathrm{PP}/{\Delta}\mathrm{PP}_{0}),$
1
in which ΔPP0 is an incremental threshold and K is a scaling constant. These parameters, obtained by regression analysis, were not significantly different between results obtained with single odd events and increase-and-hold patterns (Fig. 4B; t-test, P<0.01). In addition, the mean of the differences between the amplitudes of the novelty responses evoked by the two stimulus patterns in each pair was zero (paired t-test, P<0.001, N=22 pairs, fish 1; N=12 pairs, fish 2).
### Discrimination function and scaling of the response are independent of the contrast baseline
The general rule is that discrimination threshold increases with the baseline amplitude (following a function characteristic of the considered sensory system; Werner, 1980). This kind of rule would imply a dependence on the absolute value of the contrasts of the compared images. It has been also speculated that fish compare images pulse-to-pulse, against a fixed template(Moller, 1995), or have theability to remember what the current flow through its skin would look like in the undisturbed condition and be able to compare at this site the field in the presence of shadows from objects'(Hopkins, 1983).
In a second set of experiments we tested the hypothesis that the described function parameters are baseline dependent. As shown in Fig. 5, the relationship between ΔPP and the amplitude and probability of the novelty response was independent of the reafferent image baseline contrast. For data obtained starting from any given contrast baseline, the threshold(ΔPP0) and scaling constant (K) were similar to values calculated from the pooled data of the same fish (ANOVA-test, P>0.1, Fig. 5A). For the overall population of the seven fish, means and standard deviations(S.D.) of these parameters obtained from pooled data for each fish were:ΔPP0=18±12 mV cm-1 and K=0.13±0.07.
We also measured the probability of evoking a novelty response as a function of ΔPP. Changes in object resistance induced ΔPP of different amplitudes, ranging from -120 mV to +120 mV. Each amplitude change was induced from different baseline contrasts (10-20 trials for each ΔPP and each baseline contrast). Novelty responses occurred only for ΔPP larger than 4-8 mV cm-1. This ΔPP was comparable to thespontaneous' variation of the local signal due to respiration and other small movements. As illustrated in Fig. 5B, the probability of evoking a novelty response was a sigmoidal function of ΔPP. This function was the same for every baseline contrast. Thus, unlike other sensory systems, the critical factor for evoking a novelty response was the absolute increase above the baseline contrast rather than a function of the baseline contrast. The contrast increment that evoked novelty responses in 50% of the cases (T50) was characteristic for each fish (ranging between 5 and 25 mV cm-1). It is worth noting that ΔPP0 and T50 yielded similar values,despite being estimated by different methods(Fig. 5A,B). It is also important to recall that ΔPP0 was similar when explored with a single odd event pattern or with an increase-and-hold pattern in the same fish (Fig. 4B).
### Threshold and scaling constant depend on the preceding temporal pattern of stimulation
The experiments illustrated in Figs 4 and 5 show that the difference in contrast between the baseline and the very first image that surpasses an incremental threshold value determines the amplitude of the orienting responses according to a logarithmic law. This relationship is baseline independent. It should be noted that the same change in contrast can be achieved by flattening a top-inward' Mexican-hat' profile or increasing atop-outward' Mexican-hat' profile. These results indicate that G. carapo is permanently evaluating the change of the stimulus pattern independently of the baseline contrast. This means that the fish does not compare incoming images with a fixed template. Moreover, this suggests that novelty responses result from the comparison of the neural response to the very first altered electric physical image with a central representation of the past sensory input. This leads to the question of how many images contribute to such representation. In the third type of experiments we tested the hypothesis that fish evaluate PP in a pulse-to-pulse manner, simply comparing the contrast of each image with that of the immediately preceding image. We found that this is not the case(Fig. 6). Novelty response amplitude is a function of the number of images of the same baseline contrast that precedes the change in contrast. In these experiments, we changed the duty cycle regulating the relative timing of baseline and comparison stimulus periods without altering the total trial duration(Fig. 6 inset). Object resistance was alternated between 470 kΩ and 15 Ω to produce large changes in contrast. This procedure allowed us to control the number of EODs included in the baseline and comparison periods of the trial. Novelty response amplitude increased with the number of baseline EODs from 50 to 900, with a maximum slope at approximately 120 EODs (representing 3-6 s, depending on pacemaker frequency). Similar results were obtained for different EOD pacemaker frequencies and for both trial duration studied (100 or 30 s),suggesting that the number of EODs, and thus the number of electrosensory images, is the relevant variable.
The increase in novelty response amplitude as a function of the number of images during the baseline period could result from changes in either the scaling constant, the threshold, or both. We addressed this issue in a fourth series of experiments (N=3 fish) in which the duration of the baseline period (r0=∞, open circuit) was set at 2,10 or 29 s, and trial duration was kept constant at 30 s. The results consistently showed that the scaling constant was an increasing function of the number of baseline EODs (Fig. 7A,B). The ΔPP0 values calculated by curve-fitting were similar for 10 and 29 s in all fish; however, curve-fitting was not a reliable method for calculating ΔPP0. Note that all amplitudes of novelty responses obtained with a baseline period of 2 s were similarly small, which is consistent with the flat profile shown in Fig. 6 for less than 80 baseline EODs.
The dependence of novelty response threshold on recent past sensory history was further studied by comparing the probability distribution functions of novelty responses for baseline periods of 29, 10, 2 and 0.5 s (including approximately 900, 300, 60 and 15 EODs). For baseline periods lasting 2, 10 and 29 s, the probability distribution curves were similar (N=3 fish, Fig. 7C). Although a small increase in T50 was consistently observed for baseline periods lasting 2 s, the change in scaling constant was the most important factor to explain the decay of the amplitude of the novelty response with this stimulation pattern. Data obtained with a very short baseline period (0.5 s)were more dispersed and had a larger T50. In these experiments there were an important number of failures even when the exploredΔPP was the maximum possible (r0=∞, open circuit, r1=0, short circuit, Fig. 7D).
Our results provide behavioural evidence that pulse fish of the family Gymnotidae are able to discriminate the change in contrast of the stimulus pattern. This implies their ability to compare electrosensory information obtained from consecutive electrosensory images.
We used the novelty response as an index of discrimination. This is an electromotor orienting behavior consisting of the transient reduction of the inter-EOD interval followed by a gradual return to baseline. The dependence of the amplitude of the novelty response on the change in stimulus indicates that occurrence of this orienting behavior is a reliable index that the stimulus has been sensed and evaluated. For this reason novelty responses have been extensively used as index of electrolocation(Bullock, 1969; Heiligenberg, 1980; Grau and Bastian, 1986; Hall et al., 1995; Zellick and von der Emde,1995; Post and von der Emde,1999). However, the failure of a sensory stimulus to evoke a novelty response does not mean that it has not been sensed. In fact, our experiments show that the interval variability can be modified by a change in image contrast even though it might not evoke novelty responses. Therefore, it is important to establish first what kind of information is obtained by analyzing the amplitude and probability of the novelty response as a function of the change in electric image contrast.
The function relating probability and change in image contrast is the same when starting the experiment from different baseline image contrasts. It is important to note that the compared images consist of spatial modulations of the self-generated electrosensory carrier, which provides a basal effective stimulus for electroreceptors. This indicates that the observed behavioural threshold is not set by the electroreceptor threshold. It also suggests that the response to the comparison stimulus should be contrasted with the response to the baseline stimulus by a sensory readout mechanism somewhere in the central nervous system. The observation that the effect of a single odd event is the same as the effect of an increase-and-hold temporal pattern indicates that only the response to the very first event of the comparison stimulus train (actual input) is contrasted with the response to the baseline input. By contrast, Heiligenberg (1980)found that a change of at least two or three images is necessary to elicit novelty responses in B. occidentalis. Differences between studied species and experimental designs might account for the discrepancies. While Heiligenberg's (1980) strategy was to add artificial background noise against which a single relatively broad and blurred image generated on the side of the fish was compared, our results were obtained by changing the contrast of smaller and sharper images on the electrosensory fovea.
Our finding of a function relating the amplitude of novelty response to the change in image contrast indicates that the above-mentioned read-out mechanism provides the electromotor system with the relevant input for controlling the amplitude of the novelty response. Thus, the changes in the parameters of the described function were used to study the dynamic effects of stimulus presentation.
As occur with the probability function, the parameters of the amplitude function are the same for different baseline contrasts held constant for a long period. This is opposite to the common finding across most sensory systems where the discrimination threshold generally depends on the baseline stimulus (Weber and Fechner's and Stevens' laws; Werner, 1980). For baselines equal or larger than 2 s the amplitude of the novelty response was scaled with contrast increase, according to a baseline-duration-dependent rule(Fig. 7B). For the same change in contrast, the amplitude of the novelty response gradually decreased as the fraction of baseline period in the total cycle of stimulation was shortened(Fig. 6). This suggests that the amplitude of the novelty response is influenced by a long-lasting stimulation period including baseline images and also images belonging to the comparison period of the preceding trial. The most important reduction of the response was observed when the baseline period included less than 80-100 EODs(2-4 s), but some influence was detected up to 900 EODs (29 s), indicating that the relative importance of an electrosensory image on the transference function parameters fades out as the following images are integrated in a central expectation signal.
The threshold is significantly affected by past input only when the baseline period is shorter than 2 s (including up to 60 EODs). This period might correspond to the certain minimal period of time to stabilize and update a central state or template' of electroreceptive afferences on the background of which local novelties can be more readily discerned' as described by Heiligenberg(1980). However, our results suggest that threshold for eliciting novelty responses is not the best parameter for extracting information about sensory processing. Threshold is independent of previous history, except when the increase in image contrast is just preceded by a decrease in image contrast. The interaction of two successive, opposite and different lasting effects (the increase in image contrast eliciting otherwise a novelty response and the preceding decrease in image contrast generating a longer lasting effect indicated by the increase in interval variability) might explain this change in threshold. By contrast, the scaling constant appears to be a reflection of sensory processing features such as the generation of a central template. In fact, while the certainty of provoking a novelty response is only affected by the contrast of the few preceding images, the amplitude of the novelty response is affected by the contrast of images occurring up to half a minute before. The scaling constant is an increasing function of the number of baseline images for all the explored range of baseline duration, which suggests that the central expectation signal or template' is renewed with a much longer constant than previously calculated based on threshold analysis (60 EODs versushundreds of EODs).
Our results support the hypothesis of a template' generation initially proposed by Heiligenberg(1980), but reject the hypothesis of a fixed template, or a pulse-to-pulse comparison of the incoming images. In addition, study of the transference function of the electrosensory—electromotor transformation indicates that the scaling constant of this function is the most sensitive parameter for evaluating the template dynamics. The growth of this parameter with the number of low contrast baseline images indicates that the relative load of a given image in creating the template' fades as consecutive EODs continue to occur.
The most likely structure suited for storage and comparison of sensory responses is the electrosensory lobe. The principal output cells of this cerebellum-like structure are driven by the integration of electrosensory inputs with the parallel fiber input coming from other sensory and motor structures, as well as serving feed-back from higher level electrosensory structures (Réthelyi and Szabo,1973; Maler, 1973, 1979; Bell et al., 1997b; Berman and Maler, 1999). This type of circuit fulfils the requirements to act as the kind of comparator between input and internal sensory representations proposed by Sokolov(1990). Recordings from single cells in the electrosensory lateral line lobe of mormyrids(Bell, 1981; Bell et al., 1993, 1997a,b,c),wave type gymnotids (Bastian, 1995a,b, 1996a,b, 1998, 1999) and elasmobranch(Bodznick et al., 1992, 1999; Bodznick, 1993; Montgomery and Bodznick, 1995)have demonstrated that sensory expectations — mirror imaging the moving average of the past sensory input — cancel out expected inputs and boost novel inputs. It is important to note that this process does not rule out other synergistic mechanisms such as peripheral receptor adaptation(Xu et al., 1996) or further processing at higher levels of the electrosensory pathway. In fact, Grau and Bastian (1986) found thatmost units studied in the torus semicircularis showed very strong,increased responsiveness' to novel stimuli.
Unlike gymnotid and mormyrid wave fish, exhibiting continuous sine-wave-like EODs (Bass,1986), pulse fish electrosensory system must identify a change in the images generated by the fish's own EOD involving an additional associated task. Pulse mormyrids compare and update the reafferent information in a pulse-to-pulse manner by a plastic change of an electromotor command corollary discharge signal interacting with the reafferent electrosensory input (Bell, 1981, 1982, Bell et al., 1993, 1997a). However, in G. carapo, as well in other pulse gymnotids, there is no evidence of a pacemaker corollary discharge(Heiligenberg, 1980; Bastian, 1986; Castelló et al., 1998). The presence of a well-timed expectation signal independent of an electromotor corollary discharge is reflected in the occurrence of omitted stimulus potentials' when stopping repetitive electrosensory stimuli in elasmobranch(Bullock et al., 1990). This phenomenon, signaling the time during which the omitted sensory input should have occurred, is widespread in nature; it is observed in both vertebrates and invertebrates, from the very peripheral to the highest levels of sensory processing (Bullock et al., 1990, 1993; Karamürsel and Bullock, 1994, 2000; Ramon et al., 2001), and it might underline the central expectation mechanism suggested by our data. However, invasive techniques will be required to elucidate whether and how pulse-discharging gymnotids simultaneously deal with detection, storage,comparison and discrimination of reafferent and exafferent signals.
The stereotyped time course of the novelty response is independent of the stimulus pattern, suggesting that this behaviour is probably not completely organized within electrosensory structures. Transient accelerations of the pacemaker frequency are elicited not only by reafferent electrosensory signals but also by exafferent signals of various sensory modalities, which indicates that the electromotor control of pacemaker is the final common path of an alert system triggered by novel sensory stimuli. Theoretical and experimental studies of pacemaker structures show that the interval between pulses is a logarithmic function of pacemaker input(Hansel et al., 1998). Thus,to fit the present results it should be considered that pacemaker cells, which set the timing of the EOD, might introduce the logarithmic rule.
In conclusion, we propose the following hypothesis to explain the sensory-motor integration of the novelty response: (1) the central nervous system of the fish computes the difference between the response to each incoming electric reafferent image and a central expectation signal' ortemplate' that is repetitively updated with each EOD; (2) the novelty response is triggered by a threshold-based decision process; (3) once threshold is achieved, the amplitude of the novelty response is determined by the difference between the template' and the response to the reafferent input; (4) the relaxation curve following the initial shortening of the interval is determined by the electromotor side of the system. The creation of the template' and the comparison process are most probably carried out on the sensory side in electrosensory lateral line lobe. The triggering decision and the logarithmic scaling processes are probably carried out at the pre-pacemaker and pacemaker structures, respectively.
We thank Drs T. H. Bullock, C. Bell, C. Cerveñasky, K. Grant, J. A. Hoffer, J. P. Segundo and O. Trujillo-Cenóz for their critical reading and valuable comments on a previous version of this manuscript. This work was partially supported by Premio Clemente Estable no. 4014, Fogarty grant no. 1R03-TW05680-01 and PEDECIBA (doctorate fellowship to P.A.).
Aguilera, P. A. and Caputi, A. A. (
2003
). Electroreception in G. carapo: detection of changes in waveform of the electrosensory signals.
J. Exp. Biol.
206
,
989
-998.
Aguilera, P. A., Castelló, M. E. and Caputi, A. A.(
2001
). Electroreception in Gymnotus carapo: differences between self-generated and conspecific-generated signal carriers.
J. Exp. Biol.
204
,
185
-198.
Bass, A. H. (
1986
). Electric organs revisited. In
Electroreception
(ed. T. H. Bullock and W. Heiligenberg), pp.
13
-70. New York:Wiley.
Bastian, J. (
1986
). Electrolocation. In
Electroreception
(ed. T. H. Bullock and W. Heiligenberg), pp.
577
-612. New York:Wiley.
Bastian, J. (
1995a
). Electrolocation. In
The Handbook of Brain Theory and Neural Networks
(ed. M. A. Arbib), pp.
352
-356. Cambridge, London,Massachusetts: A Bradford Book. The MIT Press.
Bastian, J. (
1995b
). Pyramidal-cell plasticity in weakly electric fish: a mechanism for attenuating responses to reafferent electrosensory inputs.
J. Comp. Physiol. A
176
,
63
-78.
Bastian, J. (
1996a
). Plasticity in an electrosensory system. I. General features of a dynamic sensory filter.
J. Neurophysiol.
76
,
2482
-2496.
Bastian, J. (
1996b
). Plasticity in an electrosensory system. II. Postsynaptic events associated with a dynamic sensory filter.
J. Neurophysiol.
76
,
2497
-2507.
Bastian, J. (
1998
). Plasticity in an electrosensory system. III. Contrasting properties of spatially segregated inputs.
J. Neurophysiol.
79
,
1839
-1857.
Bastian, J. (
1999
). Plasticity of feedback inputs in the apteronotid electrosensory system.
J. Exp. Biol.
202
,
1327
-1337.
Bell, C. C. (
1981
). An efference copy which is modified by reafferent input.
Science
214
,
450
-453.
Bell, C. C. (
1982
). Properties of a modifiable efference copy in electric fish.
J. Neurophysiol.
47
,
1043
-1056.
Bell, C. C., Caputi, A., Grant, K. and Serrier, J.(
1993
). Storage of a sensory pattern by anti-Hebbian synaptic plasticity in an electric fish.
90
,
4650
-4654.
Bell, C. C., Caputi, A. A. and Grant, K.(
1997a
). Physiology and plasticity of morphologically identified cells in the mormyrid electrosensory lobe.
J. Neurosci.
17
,
6409
-6423.
Bell, C. C., Bodznick, D., Montgomery, J. and Bastian, J.(
1997b
). The generation and substraction of sensory expectations within cerebellum like structures.
Brain Behav. Evol.
50
,
17
-31.
Bell, C. C., Han, V. Z., Sugawara, S. and Grant, K.(
1997c
). Synaptic plasticity in a cerebellum-like structure depends on temporal order.
Nature
387
,
278
-281.
Berman, N. J. and Maler, L. (
1999
). Neural architecture of the electrosensory lateral line lobe: adaptation for coincidence detection, a sensory searchlight, and frequency-dependent adaptive filtering.
J. Exp. Biol.
202
,
1243
-1253.
Bodznick, D. (
1993
). The specificity of an adaptive filter that suppresses unwanted re-afference in electrosensory neurons of the skate medulla.
Biol. Bull.
185
,
312
-314.
Bodznick, D., Montgomery, J. and Bradley, D. J.(
1992
). Suppression of common mode signals within the electrosensory system of the little skate Raja erinacea.
J. Exp. Biol.
171
,
107
-125.
Bodznick, D., Montgomery, J. and Carey, M.(
1999
). Adaptive mechanisms in the elasmobranch hindbrain.
J. Exp. Biol.
202
,
1357
-1364.
Budelli, R. and Caputi, A. A. (
2000
). The electric image in weakly electric fish: perception of objects of complex impedance.
J. Exp. Biol.
203
,
481
-492.
Bullock, T. H. (
1969
). Species differences in effect on electroreceptor input on electric organ pacemakers and other aspects of behaviour in electric fish.
Brain Behav. Evol.
2
,
85
-118.
Bullock, T. H. (
1986
). Significance of findings on electroreception for general neurobiology. In
Electroreception
(ed. T. H. Bullock and W. Heiligenberg), pp.
651
-674. New York:Wiley.
Bullock, T. H. (
1999
). The future research on electroreception and electrocommunication.
J. Exp. Biol.
202
,
1455
-1458.
Bullock, T. H., Hofmann, M. H., Nahm, F. K., New, J. G. and Prechtl, J. C. (
1990
). Event-related potential in the retina an optic tectum of fish.
J. Neurophysiol.
64
,
903
-914.
Bullock, T. H., Karamürsel, S. and Hofmann, M. H.(
1993
). Interval specific event-related potential to omitted stimuli in the electrosensory pathway in elasmobranchs: an elementary form of expectation.
J. Comp. Physiol. A
172
,
501
-510.
Caputi, A. and Budelli, R. (
1995
). The electric image in weakly electric fish: I. A data-based model of waveform generation in Gymnotus carapo.
J. Comput. Neurosci.
2
,
131
-147.
Caputi, A. A., Budelli, R., Grant, K. and Bell, C. C.(
1998
). The electric image in weakly electric fish. Physical images of resistive objects in Gnathonemus petersii.
J. Exp. Biol.
201
,
2115
-2128.
Caputi, A. A., Castelló, M. E., Aguilera, P. A. and Trujillo-Cenóz, O. (
2003
). Electrolocation and electrocommunication in pulse gymnotids: signal carriers, pre-receptor mechanisms and the electrosensory mosaic.
J. Physiol.(Paris)
, in press.
Castelló, M. E., Caputi, A. A. and Trujillo-Cenóz,O. (
1998
). Structural and functional aspects of the fast electrosensory pathway in the electrosensory lateral line lobe of the pulse fish Gymnotus carapo.
J. Comp. Neurol.
401
,
549
-563.
Castelló, M. E., Aguilera, P. A., Trujillo-Cenóz,O. and Caputi, A. A. (
2000
). Electroreception in Gymnotus carapo: pre-receptor processing and the distribution of electroreceptor types.
J. Exp. Biol.
203
,
3279
-3287.
Grau, H. J. and Bastian, J. (
1986
). Neural correlates of novelty detection in weakly electric fish.
J. Comp. Physiol. A
159
,
191
-200.
Hall, C., Bell, C. C. and Zellick, R. (
1995
). Behavioral evidence of a latency code for stimulus intensity in Mormyrid electric fish.
J. Comp. Physiol. A
177
,
29
-39.
Hansel, D., Mato, G., Meunier, C. and Nelter, L.(
1998
). On numerical simulations of integrate-and-fire neural networks.
Neural. Comput.
10
,
67
-83.
Heiligenberg, W. (
1980
). The evaluation of electroreceptive feedback in a gymnotoid fish with pulse-type electric organ discharges.
J. Comp. Physiol. A
138
,
173
-185.
Hopkins, C. D. (
1983
). Functions and mechanisms in electroreception. In
Fish Neurobiology
(ed. R. G. Northcutt and R. E. Davis), pp.
215
-259. Ann Arbor:University of Michigan Press.
Karamürsel, S. and Bullock, T. H. (
1994
). Dynamics of event-related potentials to trains of light and dark flashes:responses to missing and extra stimuli in rays.
Electroencephalogr. Clin. Neurophysiol.
90
,
461
-471.
Karamürsel, S. and Bullock, T. H. (
2000
). Human auditory fast and slow omitted stimulus potential and steady state responses.
Int. J. Neurosci.
100
,
1
-20.
Kramer, B. (
1990
).
Electrocommunication in Teleost Fishes: Behavior and Experiments
. New York: Springer.
Larimer, J. L. and McDonald, J. A. (
1968
). Sensory feedback from electroreceptors to electromotor pacemaker in gymnotids.
Am. J. Physiol.
214
,
1253
-1261.
Lissmann, H. W. (
1958
). On the function and evolution of electric organs in fish.
J. Exp. Biol.
35
,
156
-191.
Maler, L. (
1973
). The posterior lateral line lobe of a Mormyrid fish — a Golgi study.
J. Comp. Neurol.
152
,
281
-299.
Maler, L. (
1979
). The posterior lateral line lobe of certain Gymnotiform fish. Quantitative light microscopy.
J. Comp. Neurol.
183
,
323
-363.
Marr, D. (
1982
). The philosophy and the approach. In
Vision
, chapter 1 (ed. J. Wilson), pp.
25
-27. New York: W. H. Freeman and Company.
Meyer, J. H. (
1982
). Behavioral responses of weakly electric fish to complex impedances.
J. Comp. Physiol. A
145
,
459
-470.
Moller, P. (
1995
).
Electric Fishes. History and Behavior
. London: Chapman and Hall.
Montgomery, J. C. and Bodznick D. (
1995
). Hindbrain circuitry mediating common mode supression of ventilatory reafference in the electrosensory system of the little skate Raja erinacea.
J. Exp. Biol.
183
,
203
-215.
Nelson, M. E. and MacIver, M. A. (
1999
). Prey capture in the weakly electric fish Apteronotus albifroms: sensory acquisition strategies and electrosensory consequences.
J. Exp. Biol.
202
,
1195
-1203.
Post, N. and von der Emde, G. (
1999
). Thenovelty response' in an electric fish: response properties and habituation.
Physiol. Behav.
68
,
115
-128.
Ramon, F., Hernández, O. and Bullock, T. H.(
2001
). Event related potentials in an invertebrate: crayfish emit omitted stimulus potentials.
J. Exp. Biol.
204
,
4291
-4300.
Rasnow, B. (
1996
). The effects of simple objects on the electric field of Apteronotus.
J. Comp. Physiol. A
178
,
397
-411.
Réthelyi, M. and Szabó, T.(
1973
). Neurohistological analysis of the lateral lobe in an electric fish Gymnotus carapo (Gymnotidae).
Exp. Brain. Res.
17
,
229
-241.
Sicardi, A. E., Caputi, A. A. and Budelli, R.(
2000
). Physical basis of electroreception.
Physica A
283
,
86
-93.
Sokolov E. N. (
1990
). The orienting response and future direction of its development.
Pavlov. J. Biol. Sci.
25
,
142
-150.
Spector, A. C. (
2000
). Linking gustatory neurobiology to behavior in vertebrates.
Neurosci. Biobehav. Rev.
24
,
391
-406.
Stoddard, P. K., Rasnow, B. and Assad, C.(
1999
). Electric organ discharges of the gymnotiform fishes: III. Brachyhypopomus.
J. Comp. Physiol. A
184
,
609
-630.
Szabo, T. and Fessard, A. (
1965
). Le functionnement des électrorrècepteurs étudié ches les Mormyres.
J. Physiol. (Paris)
57
,
343
-360.
Trujillo-Cenóz, O., Echague, J. A. and Macadar, O.(
1984
). Innervation pattern and electric organ discharge waveform in Gymnotus carapo.
J. Neurobiol.
15
,
273
-281.
von der Emde, G. (
1990
). Discrimination of objects through electrolocation in the weakly electric fish Gnathonemus petersii.
J. Comp. Physiol. A
167
,
413
-421.
Werner, G. (
1980
). The study of sensation in physiology: psychophysical and neurophysiological correlations. In
Medical Physiology
(ed. V. B. Mountcastle), pp.
605
-628. St. Louis: The C.V. Mosby Company.
Xu, Z., Payne, J. R. and Nelson, M. E. (
1996
). Logarithmic time course of sensory adaptation in electrosensory afferent nerve fibers in a weakly electric fish.
J. Neurophysiol.
76
,
2020
-2032.
Zellick, R. and von der Emde, G. (
1995
). Behavioral detection of electric signal waveform distortion in the weakly electric fish Gnathonemus petersii.
J. Comp. Physiol. A
177
,
493
-501.
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Calculates the long-term mean, median, maximum, minimum, and percentiles of daily flow values for over all months and all data (Long-term) from a daily streamflow data set. Calculates statistics from all values, unless specified. Returns a tibble with statistics.
calc_longterm_daily_stats(
data,
dates = Date,
values = Value,
groups = STATION_NUMBER,
station_number,
percentiles = c(10, 90),
roll_days = 1,
roll_align = "right",
water_year_start = 1,
start_year,
end_year,
exclude_years,
months = 1:12,
complete_years = FALSE,
include_longterm = TRUE,
custom_months,
custom_months_label,
transpose = FALSE,
ignore_missing = FALSE
)
## Arguments
data Data frame of daily data that contains columns of dates, flow values, and (optional) groups (e.g. station numbers). Leave blank if using station_number argument. Name of column in data that contains dates formatted YYYY-MM-DD. Only required if dates column name is not 'Date' (default). Leave blank if using station_number argument. Name of column in data that contains numeric flow values, in units of cubic metres per second. Only required if values column name is not 'Value' (default). Leave blank if using station_number argument. Name of column in data that contains unique identifiers for different data sets, if applicable. Only required if groups column name is not 'STATION_NUMBER'. Function will automatically group by a column named 'STATION_NUMBER' if present. Remove the 'STATION_NUMBER' column beforehand to remove this grouping. Leave blank if using station_number argument. Character string vector of seven digit Water Survey of Canada station numbers (e.g. "08NM116") of which to extract daily streamflow data from a HYDAT database. Requires tidyhydat package and a HYDAT database. Leave blank if using data argument. Numeric vector of percentiles to calculate. Set to NA if none required. Default c(10,90). Numeric value of the number of days to apply a rolling mean. Default 1. Character string identifying the direction of the rolling mean from the specified date, either by the first ('left'), last ('right'), or middle ('center') day of the rolling n-day group of observations. Default 'right'. Numeric value indicating the month (1 through 12) of the start of water year for analysis. Default 1. Numeric value of the first year to consider for analysis. Leave blank to use the first year of the source data. Numeric value of the last year to consider for analysis. Leave blank to use the last year of the source data. Numeric vector of years to exclude from analysis. Leave blank to include all years. Numeric vector of months to include in analysis (e.g. 6:8 for Jun-Aug). Leave blank to summarize all months (default 1:12). Logical values indicating whether to include only years with complete data in analysis. Default FALSE. Logical value indicating whether to include long-term calculation of all data. Default TRUE. Numeric vector of months to combine to summarize (ex. 6:8 for Jun-Aug). Adds results to the end of table. If wanting months that overlap calendar years (ex. Oct-Mar), choose water_year_start that begins before the first month listed. Leave blank for no custom month summary. Character string to label custom months. For example, if months = 7:9 you may choose "Summer" or "Jul-Sep". Default "Custom-Months". Logical value indicating whether to transpose rows and columns of results. Default FALSE. Logical value indicating whether dates with missing values should be included in the calculation. If TRUE then a statistic will be calculated regardless of missing dates. If FALSE then only those statistics from time periods with no missing dates will be returned. Default FALSE.
## Value
A tibble data frame with the following columns:
Month
month of the year, included 'Long-term' for all months, and 'Custom-Months' if selected
Mean
mean of all daily data for a given month and long-term over all years
Median
median of all daily data for a given month and long-term over all years
Maximum
maximum of all daily data for a given month and long-term over all years
Minimum
minimum of all daily data for a given month and long-term over all years
P'n'
each n-th percentile selected for a given month and long-term over all years
Default percentile columns:
P10
annual 10th percentile selected for a given month and long-term over all years
P90
annual 90th percentile selected for a given month and long-term over all years
Transposing data creates a column of "Statistics" and subsequent columns for each year selected.
## Examples
# Run if HYDAT database has been downloaded (using tidyhydat::download_hydat())
# Calculate long-term statistics using data argument with defaults
flow_data <- tidyhydat::hy_daily_flows(station_number = "08NM116")
calc_longterm_daily_stats(data = flow_data,
start_year = 1980)
# Calculate long-term statistics using station_number argument with defaults
calc_longterm_daily_stats(station_number = "08NM116",
start_year = 1980)
# Calculate long-term statistics regardless if there is missing data for a given year
calc_longterm_daily_stats(station_number = "08NM116",
ignore_missing = TRUE)
# Calculate long-term statistics for water years starting in October
calc_longterm_daily_stats(station_number = "08NM116",
start_year = 1980,
water_year_start = 10)
# Calculate long-term statistics with custom years
calc_longterm_daily_stats(station_number = "08NM116",
start_year = 1981,
end_year = 2010,
exclude_years = c(1991,1993:1995))
# Calculate long-term statistics for 7-day flows for July-September months only,
# with 25 and 75th percentiles
calc_longterm_daily_stats(station_number = "08NM116",
roll_days = 7,
months = 7:9,
percentiles = c(25,75),
ignore_missing = TRUE,
include_longterm = FALSE) # removes the Long-term numbers
# Calculate long-term statistics and add custom stats for July-September
calc_longterm_daily_stats(station_number = "08NM116",
start_year = 1980,
custom_months = 7:9,
custom_months_label = "Summer")
}
#> Warning: One or more calculations included missing values and NA's were produced. Filter data for complete years or months, or use to ignore_missing = TRUE to ignore missing values.#> # A tibble: 14 x 8
#> STATION_NUMBER Month Mean Median Maximum Minimum P10 P90
#> <chr> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 08NM116 Jan 1.16 0.940 9.5 0.160 0.570 1.78
#> 2 08NM116 Feb 1.19 0.971 5.81 0.140 0.561 2.00
#> 3 08NM116 Mar 1.89 1.36 17.5 0.380 0.704 3.71
#> 4 08NM116 Apr 8.65 6.51 53.5 0.505 1.45 18.5
#> 5 08NM116 May 24.6 22.4 80.8 2.55 9.73 42.7
#> 6 08NM116 Jun 22.0 19.7 86.2 0.450 6.10 39.7
#> 7 08NM116 Jul 6.28 3.90 76.8 0.332 1.12 14.0
#> 8 08NM116 Aug 2.03 1.54 13.3 0.427 0.836 3.84
#> 9 08NM116 Sep 2.10 1.58 14.6 0.364 0.770 4.11
#> 10 08NM116 Oct 2.06 1.64 15.2 0.267 0.841 3.82
#> 11 08NM116 Nov 2.01 1.62 11.7 0.260 0.590 3.99
#> 12 08NM116 Dec 1.29 1.06 7.30 0.244 0.528 2.27
#> 13 08NM116 Long-term 6.28 1.83 86.2 0.140 0.705 20
#> 14 08NM116 Summer 3.48 1.90 76.8 0.332 0.863 7.20
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# Definition:Relation/Notation
## Definition
Let $\RR$ be a relation.
If $\tuple {x, y}$ is an ordered pair such that $\tuple {x, y} \in \RR$, we use the notation:
$s \mathrel \RR t$
or:
$\map \RR {s, t}$
and can say:
$s$ bears $\RR$ to $t$
$s$ stands in the relation $\RR$ to $t$
If $\tuple {s, t} \notin \RR$, we can write: $s \not \mathrel \RR t$, that is, by drawing a line through the relation symbol.
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mersenneforum.org LLRnet server rally 400
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2008-06-16, 17:41 #1 mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 3·2,083 Posts LLRnet server rally 400
2008-06-16, 18:02 #2 kar_bon Mar 2006 Germany 2×1,433 Posts i will throw in all cores of my quad, perhaps one other smaller core. currently running on IB400 server, can change to A300 as well. and another hint: to avoid many 'open' pairs after the rally, please everyone be sure to clear the workfile of all clients, so we have not to wait some days for a second submission of these pairs. thanks.
2008-06-16, 18:13 #3 mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 3·2,083 Posts Here's a table representing all the cores that users plan to bring to the rally, which I will try to keep updated as more people provide this information: Code: `User Cores Range preference Server ----------------------------------------------------------- Anonymous 2 fast 400
2008-06-16, 18:35 #4 Flatlander I quite division it "Chris" Feb 2005 England 81D16 Posts I'll bring 4 fast cores to 400
2008-06-16, 18:52 #5 gd_barnes May 2007 Kansas; USA 1027910 Posts I was going to suggest delaying the rally 1-2 weeks. I'm out of town again this coming weekend but will be back in town the following 2 weekends. If it's this weekend, I can only bring 5 cores. I'm still not going to have time to set up the remote desktop before I leave and I have too many other reservations to stop them for 8 days and put all my cores on the rally servers for that long of a period. What hurt me was the power outage that I had 3 hours after I left last time for 8 days. My 28 cores were idled for almost the entire time leaving all of my reservations well behind where they should be. Gary Last fiddled with by gd_barnes on 2008-06-16 at 18:52
2008-06-16, 19:13 #6
mdettweiler
A Sunny Moo
Aug 2007
USA (GMT-5)
3·2,083 Posts
Quote:
Originally Posted by gd_barnes I was going to suggest delaying the rally 1-2 weeks. I'm out of town again this coming weekend but will be back in town the following 2 weekends. If it's this weekend, I can only bring 5 cores. I'm still not going to have time to set up the remote desktop before I leave and I have too many other reservations to stop them for 8 days and put all my cores on the rally servers for that long of a period. What hurt me was the power outage that I had 3 hours after I left last time for 8 days. My 28 cores were idled for almost the entire time leaving all of my reservations well behind where they should be. Gary
Unfortunately, the next two weekends won't work for me at all. I'll be taking a weeklong vacation from the ~28th to the ~5th (not sure exactly which days I'll be leaving and returning), and may or may not have any access to mersenneforum at all. If I do have any access, it will be quite limited, and I won't have any access to my results processing tools whatsoever. Most likely I'll only have one or two older laptops with me on vacation, and they'll only be able to connect through dial-up, so no remote controlling my home machine to use my processing tools.
By contrast, Gary, you have a moderate degree of mersenneforum access on your trips, so it should theoretically have a lesser impact on the rally if you weren't home than if I wasn't home.
So, how about we have the rally this weekend, and then hold off on our next one until I am back--that way, we'll have the maximum possible amount of admin personnel on hand during the rally. Gary, considering the situation with your various reservations, don't fret about how many cores you put on the rally--just put on what you can spare, don't worry about have reservations make way for the rally.
2008-06-16, 19:55 #7 Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 426710 Posts I'll bring my two Athlon X2 2.5 GHz cores to it, whatever time it is (as always). I guess you'd consider that fast (at n=485K, 32K FFT, I take ~455 seconds per pair). I'll run it on 400 485
2008-06-16, 20:13 #8 em99010pepe Sep 2004 2×5×283 Posts Anon, My server is up and running. Mini-Geek, That's slow, I get 224 seconds with LLRnet on n=511k (drive 3). Edit: Tested the server and I get 226 seconds on n=505k 400
2008-06-16, 22:37 #9
mdettweiler
A Sunny Moo
Aug 2007
USA (GMT-5)
3·2,083 Posts
Quote:
Originally Posted by em99010pepe Anon, My server is up and running. Mini-Geek, That's slow, I get 224 seconds with LLRnet on n=511k (drive 3). Edit: Tested the server and I get 226 seconds on n=505k 400
Great! I've already added it to the "LLRnet Servers for NPLB" thread; I'll add it to the first post of this thread as soon as I submit this post.
2008-06-16, 22:43 #10
mdettweiler
A Sunny Moo
Aug 2007
USA (GMT-5)
3·2,083 Posts
Quote:
Originally Posted by Mini-Geek I'll bring my two Athlon X2 2.5 GHz cores to it, whatever time it is (as always). I guess you'd consider that fast (at n=485K, 32K FFT, I take ~455 seconds per pair). I'll run it on 400
Okay, yeah, that sounds like a good idea. I'll add that field to the table shortly. (For those who don't really care which server within a given range you go on, just pick whichever one has the least amount of people on it already.)
If you have more than one core in the rally, though, you may want to considering balancing out your cores over all the servers in your chosen range. I'm planning to put one of my cores on one server and the other on another (I'll play it by ear as to which server I go on, based on which ones have the lowest load at the time I switch my cores over to rally configuration). This can also provide some failover protection, so that if one server goes down at least part of your machine is idle.
If anyone else plans to wait and see which server has the lowest load, and go on that (rather than picking out a server ahead of time) just say so and I'll mark you with a * in the server field in the table.
2008-06-17, 05:25 #11
gd_barnes
May 2007
Kansas; USA
19·541 Posts
Quote:
Originally Posted by Anonymous Unfortunately, the next two weekends won't work for me at all. I'll be taking a weeklong vacation from the ~28th to the ~5th (not sure exactly which days I'll be leaving and returning), and may or may not have any access to mersenneforum at all. If I do have any access, it will be quite limited, and I won't have any access to my results processing tools whatsoever. Most likely I'll only have one or two older laptops with me on vacation, and they'll only be able to connect through dial-up, so no remote controlling my home machine to use my processing tools. By contrast, Gary, you have a moderate degree of mersenneforum access on your trips, so it should theoretically have a lesser impact on the rally if you weren't home than if I wasn't home. So, how about we have the rally this weekend, and then hold off on our next one until I am back--that way, we'll have the maximum possible amount of admin personnel on hand during the rally. Gary, considering the situation with your various reservations, don't fret about how many cores you put on the rally--just put on what you can spare, don't worry about have reservations make way for the rally.
That's fine. I'll put my 5 cores on port 300 (currently on port 400) shortly before I leave in the morning. It has the most remaining work at the moment and I'm sure you'll keep it loaded up if it runs low.
Is there a way we can have Beyond in the rally? In other words, is there a way to count how much he processes of his 486K-496K range during the rally hours?
Gary
Last fiddled with by gd_barnes on 2008-06-17 at 05:27
Similar Threads Thread Thread Starter Forum Replies Last Post gd_barnes No Prime Left Behind 61 2010-07-30 17:28 mdettweiler No Prime Left Behind 66 2008-08-11 03:00 gd_barnes No Prime Left Behind 172 2008-06-04 19:21 gd_barnes No Prime Left Behind 45 2008-05-05 19:56 gd_barnes No Prime Left Behind 135 2008-03-14 19:52
All times are UTC. The time now is 17:20.
Tue Jan 19 17:20:04 UTC 2021 up 47 days, 13:31, 0 users, load averages: 2.59, 2.47, 2.32
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## Stream: new members
### Topic: reduce iff?
#### Thorsten Altenkirch (Oct 01 2020 at 12:30):
For the purposes of illustrations I tried
variables P Q R : Prop
#reduce ¬ P
#reduce P ↔ Q
while ¬ P reduces to P → false, P ↔ Q is not unfolded to (P → Q) ∧ (Q → P) as I hope. Why is this?
#### Thorsten Altenkirch (Oct 01 2020 at 12:30):
I guess it is an inductive definition?
#### Anne Baanen (Oct 01 2020 at 12:34):
Indeed:
#print notation ↔
-- _ ↔:20 _:20 := iff #1 #0
#print iff
/-
structure iff : Prop → Prop → Prop
fields:
iff.mp : ∀ {a b : Prop}, (a ↔ b) → a → b
iff.mpr : ∀ {a b : Prop}, (a ↔ b) → b → a
-/
#### Kevin Buzzard (Oct 01 2020 at 14:08):
You can do cases on it though :-)
Last updated: May 13 2021 at 00:41 UTC
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# How do electrons know when a circuit is closed?
I was told that electrons do not begin flowing unless the circuit is closed. The electrons from the battery are not in the ends of wire when it is open, apparently, as there is no reason for them to go there. They do not "test the waters", so to speak. So how do they "know" when the circuit is closed?
Also, when do they know? Do they know the instant it is closed? Please resolve this vexing problem for me.
• The most important thing to remember is, as @JoshuaLin said, that electrons are always "testing the water". That's the case with any particle in a high potential region of space (that potential could be due to gravitational field or electric field). – Milind R Jul 11 '16 at 9:39
• @MilindR Also pressure potential. The "testing the waters" might even be easier to understand for pressure; where you can get a more tangible sense of how the potential is always waiting to go somewhere lower. – JMac Feb 12 '18 at 21:56
The electrons from the battery are not in the ends of the wires, no. The wires do contain electrons, however. Conductors have free electrons which can "float" around in the metal. There is an electric field between the two terminals of the battery. The electrons experience a force due to this field. When the wire is not connected, the electrons don't go anywhere because there isn't a path for them to flow around. Imagine one end of the wire being connected to the negative terminal of the battery and the other end of the wire brought very close to touching the positive terminal. The electric field is going to cause the electrons to move toward the positive terminal of the battery. Since there isn't a closed path for them to flow, the electrons are going to "bunch up" at the end of the wire close to the positive terminal. The displaced charge will produce it's own electric field that will exactly cancel the electric field from the battery, and the charges will stop building up on the end of the wire. When the battery is connected, there is a path for the electrons to flow and all the built up charge is absorbed into the battery. Since there is a closed path for the electrons to flow around the circuit, there is no way for a charge to build up that opposes the electric field of the battery. So, a current flows.
• This still draw on the somehow magic thinking that "it flows because there is a (macroscopic) path", without answering the question of what this workable path emerge from. – Fabrice NEYRET Oct 29 '15 at 11:54
• As I explained, an open circuit allows charges to build up which oppose the electric field that would be driving current around the circuit. When the circuit is closed, there is nowhere for charges to build up. – Robert Stiffler Oct 29 '15 at 12:02
• Yes. But the point is in expliciting more what happen at each location in the wire, along the transitional front, at the moment you close the circuit. How global circulation will results on piles of local interactions (well, like for many others phenomenons. E.g. it's interesting to really decompose locally what makes a balloon rise, because "floatability" is really not a constructive answer. Also, natural convection is very difficult to start in simulations, and it's interesting to understand why (and why it works in nature). And indeed it's not as simple as it looks.) – Fabrice NEYRET Oct 29 '15 at 12:16
As long as you provide a power source to a circuit, whether it is closed or not, electrons will definitely begin to move to a small amount. There are two specific cases which I think would best demonstrate this point.
Case 1: A circuit with a capacitor.
A simple capacitor contains two electrically conducting plates separated by an insulator, which could be for example air. In real life, a capacitor could simply be two sheets of copper parallel to each other, but not touching. An analysis of a circuit containing a capacitor, such as the above shown RC circuit, shows however that current DOES still flow, even though the circuit is not 'closed' in the sense that you mean it. You might ask "how does current flow, if there is a gap of air between the capacitor plates?" and the answer is that the current that flows is minimal, and the charge that is moved builds up on the capacitor plates, until the voltage from the charges on the capacitor cancels out the voltage from the battery. Hence, a better explanation is to think that the electrons are always testing the water (in particular, the electric field throughout the circuit).
Case 2: A really big circuit
Ultimately, the reason that electrons travel through the wire in the first place is because of the electric field that exists throughout space. In the case of a really big circuit, if you imagine that initially the circuit is closed and there is a constant current flowing and I get a pair of scissors and cut a part of the wire, 99% of the other electrons just won't care that the circuit is now open. From the electron's point of view, the world looks just like it did before the cut, the power source is still there, the loop of wire is still there, the only difference being a single break in the circuit, which does nothing (as of yet) to affect the electric field. They'll keep on travelling about the circuit just as they did before. Eventually, however, they'll build up at one end of the cut wire, and THEN the situation will change, and the current will stop. My point is that the circuit being open doesn't inherently mean that no electrons will flow.
• liked your answer because is the only only one not applying antropomorphic properties to electrons as the base of the answer, such us how they "know", "feel", "want". – jotadepicas Oct 30 '15 at 10:23
Keep in mind that for whatever magical reason electrons repel each other (like charges), and are very attracted to protons (opposite charges). Due to the omni-directional bonding present with metals (electron sea model) electrons move freely around but the metal maintains a net charge of zero.
Try not to think of the electrons as "testing the water." I find it much easier to think of circuits from the battery's point of view. Due to the laws of chemistry the battery wants to maintain a 1:1 ratio of electrons and protons. Think of it like a tug of war. The positive end starts pulling but no work is being done, and the negative end keeps pushing put no work it done. The negative end cannot give an electron unless the positive end receives one. That is why the electrons in the wire create a net movement, even if the the electrons originally in the battery decide to never come back, for every one that "joins" the wire another one is "pushed" out. Don't forget that the battery is not picky where its electrons go or come from, just as long as it gets one back for every one it loses.
• Very apt explanation, but I'd say that the electrons "testing the water" AND the battery "pulling electrons from the positive terminal and pushing them out of the negative one" together give the right intuition. Your answer concentrates on the battery, and Joshua Lin's focuses on the transmission of electricity. – Milind R Jul 11 '16 at 9:43
I was told that electrons do not begin flowing unless the circuit is closed.
The electrons from the battery are not in the ends of wire when it is open,
The electrons involved in electric current are present throughout the metal wire. They are not supplied by the battery into an "empty" wire. The metal in the wire is awash with free electrons.
apparently, as there is no reason for them to go there.
There is no need for electrons from the battery to be present at the other ends of the wire, the metal of the wire contains vast numbers of free electrons.
They do not "test the waters", so to speak. So how do they "know" when the circuit is closed?
They respond to the electric field.
Note that if the far end of the wire is unconnected, electrons do not significantly accumulate there under the influence of the electric field of the battery because, apart from anything else, a large accumulation of electrons would repel one another and prevent newer electrons joining them.
Note that in certain cases electronic engineers do have to take into account stray capacitances in wires and connectors. Beginners working with typical DC batteries and LEDs etc don't need to worry about this.
• "They respond to the electric field": magic thinking again. again, what about a light-year long wire ? – Fabrice NEYRET Oct 29 '15 at 11:57
• @Fabrice: A light-year long copper (or gold) wire would have a very high resistance. You'd need some sort of superconducting wire and a very high voltage "battery". When you connect one end of the wire to the battery it would take several years before you could hope to measure any voltage at the far end. I don't see where you are going with this. – RedGrittyBrick Oct 29 '15 at 12:08
• Just try to come back to the very question, which is important for many other transitional situation (how things start, where emerging phenomena come from). Here the length just cancels the idea that a field instantaneously appears to automagically show the way to electrons. ;-) – Fabrice NEYRET Oct 29 '15 at 12:11
To answer in a more simple fashion: the electrons in the wires feel repulsion from the other electrons. When no current in moving around, they are in a state called equilibrium. Essentially, the electrons in front of and behind our electron - let's call him the "test electron" - are stationary, so he's roughly stationary too. The forces from his neighbors all balance out. Technically, thermal energy and random fluctuations around him make him jiggle around a bit, but overall he and his friends and just sort of milling around in the same area. This is the case when the circuit is open and no current can flow.
Now, we close the circuit, completing it, and perhaps attach a battery or apply a current of some sort. In the instant this is done - mere fractions of fractions of seconds - nothing happens to test electron (assuming test electron is in the middle of the circuit). The electrons around him are also basically still for this tiny, tiny fraction of a second (unnoticable to our human senses). However, a change quickly moves through the circuit. Electrons near the battery are tugged or pushed, and their electric charge then pushes and tugs their neighboring electrons, and very quickly this force is propagated and felt through the entire circuit. Note that the speed the force travels is very quick, faster than the speed of the actual electrons, but not infinite. Electromagnetic forces are propagated by light waves, which move extremely fast.
As noted above, how much current you get is determined by Ohm's law:
V = IR or I = V/R
Here, I is our current, V our Voltage (presumably from the battery) and R the resistance of the circuit.
To think of it another way, it's like pushing a car. Technically, when you lean over and push the back bumper there's a chain reaction moving from the back of the car toward the front and the whole thing lurches forward bit by bit. However, the electric forces between atoms and molecules in the car transmit very quickly (basically close to the speed of light), so we basically see the whole car move at once.
Some people, however, take this too far and try to image building a giant rod of metal from here to another star system. They think that since they can jiggle a human sized rod and the whole thing appears to move instantaneously, that we could do the same thing to communicate between here and distant stars faster than the speed of light. However, at interstellar distances, the force that moves the atoms has to go so far (light years) that the jiggle would actually be noticeably delayed from getting from the front of the rod to the end. The force can only travel - at maximum - at the speed of light, so at several light years of distance is would take several years for the force to jiggle the end of the rod. Crazy, huh?
Hope that makes sense!
• See my comments to Fabrice's explanation below. Yours is afflicted with the same problems. Energy in wires is not being carried by electrons but by the electromagnetic field that the source will build up on the wires that are connecting it with the load. – CuriousOne Oct 29 '15 at 9:44
• @CuriousOne: Well, it's like saying pressure waves are not carried by air molecules. -> It's good physics to abstract the emerging phenomenas, but I think it's bad physics not to see the micro-phenomas it is based on. – Fabrice NEYRET Oct 29 '15 at 11:50
• Literally nowhere in my response do I directly say energy is carried by electrons. In fact, I mention electric forces and repulsion multiple times. Besides, without the electrons, we have no electric field here, and no question from OP (which is about the electrons in a wire). I assume this is why I go to stackoverflow and all the top google results for questions have 0 positive votes. Pedantry trumps simplicity, as usual. – ArtifexR Oct 29 '15 at 19:18
• @FabriceNEYRET: Electromagnetism simply doesn't work like pressure in air. If it did, you wouldn't have a computer and there would be no wireless networks. – CuriousOne Oct 29 '15 at 19:32
• @ArtifexR: The repulsion between electrons is nowhere needed to transport energy with electromagnetic waves and it is not what leads to the flow of current in circuits. It's the electric potential that leads to current flow. – CuriousOne Oct 29 '15 at 19:33
The electrons in circuits moving as a incomprehensible fluid. At least for sufficiently small electric field. So, the information of boundary on the circuit are transmitted through the electrons via equilibrium. You can imagine a lot of boxes distributed over the conductor that the circuit is made up. Each box has your own chemical potential. The information of the boundary are transmitted by fast equilibriums over this boxes.
You need to understand that a lot of transient complications happens in the middle of this conversation, but they are incredibly fast and then unimportant almost all the time. In usual time scales of electronic devices we have thermodynamic equilibrium locally through the conductors.
Take this circuit:
We have an neutral plate ($0$) connected with a battery in the positive side ($+$). At a small interval of time this system is already in equilibrium:
The charge is spread over the neutral parts. We can describe the the intermediate process by differential equation if the time scale is big enough in such a way that we can assume local thermal equilibrium. The solution of the most simple differential equation is a typical exponential on the time variable. This equation relates the charge at the plate with time. This solution already give us an particular time scale $\tau$ (Relaxation Time).
• For times $t$ much more long than $\tau$, this equation is useless and we do not appreciate any current.
• For times $t\sim\tau$ we do appreciate current and this equation dictates your behaviour.
• For times $t$ much more short than $\tau$ this equation is no more valid and things start to be more complicated.
You are basically asking when current does happen. In a macroscopic level, the answer is simple: $$\mathbf J = \sigma\mathbf E$$
We can have this equation applied to a circuital point of view, thus arriving at Ohm's Law: $$V = RI,\quad\quad I = GV.$$
The value $R$ is known as resistance, and $G$ is known as conductance.
When there is not current? Simple. When $G = 0$ or $R = \infty$. Why? Apply the law: $I = GV$. If $G=0$ then $I = 0$. So, no current if conductance is zero. Also, the higher the conductance, the higher the current, for a same potential difference $V$. Resistance and conductance are related: $V = 1/G$.
Since in real world there is no material with zero conductivity, there is always current. If conductance is too low, the current is too low as well, that can be ignored. In other words, the resistance is too high, toooo high, to have a considerable minimal current $I$.
However, when you close the circuit, you now have a high conductive path across the potential difference. Now, there will be considerable currents due to high $G$, or due to low $R$.
• I have the feeling your answer would be very useful if I understood it. I am slightly familiar with ohm's law and resistivity but I am kind of lost on the rest of what you said. We covered circuitry in one six weeks last year in physics, so sorry I don't leave you much to work with. – syzygy Oct 29 '15 at 2:35
• @syzygy I have simplified the answer. Is it better? – Physicist137 Oct 29 '15 at 2:51
• I think this answer is out of the question. The question was about the microphysics and transitory stage that explain how things get in motion. The some question could have been asked about natural convection, for instance. – Fabrice NEYRET Oct 29 '15 at 9:31
• @FabriceNEYRET Well, there is no specification anywhere that the question asks only in a microscopical level. Thus, this answer answers the question. – Physicist137 Oct 29 '15 at 11:19
• The question is around "how the electrons now knows the circuit is close and can go". So the answer cannot be "since there is a path, here is the (stationary range) law on the path". – Fabrice NEYRET Oct 29 '15 at 11:55
I could be wrong, but there is a phenomenon in physics called quantum superposition. To briefly explain it, an electron can be in all possible allowed places at once until it interacts with another particle causing, in laymen's terms, the universe to "observe" it. When a circuit is closed, the free electrons are given a specific path in which they may go, therefore they seemingly materialize and buzz through the circuit. Look at explanations of the famous "double slit experiment," quantum superposition, and wave-particle duality. These will provide much more info than I can squeeze into this paragraph.
Due to the chemical potential in the battery incitating charges to migrate, one battery end somehow suck electrons, yielding some "tension" of free electrons in the wire (slight loss in electrons). The other end somehow push, yielding some "pression" of free electrons in the wire (slight excess in electrons). If both ends are not connected because the circuit is open, an equilibrium is reached within the ends and nothing move. If they are, the excess on one end, the loss on the other end, can propagate from place to place in the wire, so that the new electrons can be suck/pushed.
• Unfortunately that's not the correct explanation, even though one finds it sometimes being presented in high school. The water analogy for electric current goes only so far and this, I am afraid, takes it way beyond the point where it's more false than it is right. The problem is that one needs a thorough understanding of electromagnetic fields for the real explanation of how currents "get moving". – CuriousOne Oct 28 '15 at 23:24
• Do you think the same about ArtifexR answer ? because I meant the same thing in simpler terms, with only the (possibly wrong) difference that I was thinking a symmetry existed on the two ends of the battery, with an excess of charge vs a loss of charge. – Fabrice NEYRET Oct 29 '15 at 9:36
• I didn't read his answer until now. Yes, it seems to be afflicted with the exact same problems. Electricity can simply not be reduced to moving charges, it has to be understood as charges reacting to electromagnetic fields. The energy transport is always in the field and not in the charges, even in the DC case. – CuriousOne Oct 29 '15 at 9:42
• I don't think this way of seeing things is valid in transitory stage, at the early moment connection is made. See also the case mentioned above about a circuit that would be light-year long. Or imagine a liquid with ions. -> I think you can really explain better (or say, also) on local-based explanations (which do produce emerging phenomena the classical laws are capturing). – Fabrice NEYRET Oct 29 '15 at 11:46
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>> Home >> Resources & support >> FAQs >> Moving the temporary directory to another hard drive
Note: This FAQ is intended for users of Stata 8 or earlier.
## Why am I getting a message that there is no room on my hard drive?
Title Moving the temporary directory to another hard drive Author Jeremy B. Wernow, StataCorp
By default, Stata will save temporary files in the directory pointed to by the TEMP (DOS) or TMPDIR (Unix) environment variable. If you are working with a large dataset, and if the hard drive or filesystem to which Stata is writing temporary files is low on space, you may get error messages saying you have no more room to perform calculations (or something similar).
If you have another hard drive or another filesystem with more space, you can change the temporary directory location to alleviate the problem.
To verify the location of the temporary directory Stata is using, you can type the following commands from within Stata:
. tempfile junk
. display "junk'"
Ignore the filename and look at the directory—this is where Stata is saving temporary files.
Windows users can reset the TEMP environment variable in DOS either before starting Stata or in the autoexec.bat (and then rebooting the computer). You just need to make sure that the directory you specify exists. In DOS, type
C:\WINDOWS> mkdir e:\temp
C:\WINDOWS> set TEMP=e:\temp
C:\WINDOWS> c:\stata\wstata.exe
Unix users can reset the TMPDIR environment variable in their shell either before starting Stata or in their .cshrc (or equivalent) shell initial settings file. In csh, type
% setenv TMPDIR /alt/tmp
`
If you now execute the same tempfile and display Stata commands mentioned above, you will see that the temporary files are now stored in the new location.
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# American Institute of Mathematical Sciences
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Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem
July 2021, 41(7): 3031-3043. doi: 10.3934/dcds.2020396
## Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source
1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China 2 College of Mathematics and Statistics, Yili Normal University, Yining 835000, China
* Corresponding author: Qiao Xin
Received June 2020 Revised October 2020 Published December 2020
Fund Project: The second author is supported by NSFC [No. 11771062, 11971082], Fundamental Research Funds for the Central Universities [No. 2019CDJCYJ001], and Chongqing Key Laboratory of Analytic Mathematics and Applications. The third author is supported by the Youth Doctor Science and Technology Talent Training Project of Xinjiang Uygur Autonomous Region [No. 2017Q087]
This paper deals with the global boundedness of solutions to the forager-exploiter model with logistic sources
$\begin{equation*} \left\{ \begin{array}{lll} u_t = \Delta u- \nabla\cdot(u\nabla w) + \mu_1 (u-u^m), &x \in \Omega, t>0,\\ v_t = \Delta v - \nabla\cdot(v\nabla u) + \mu_2 ( v-v^l), &x\in \Omega, t>0,\\ w_t = \Delta w - \lambda(u+v)w - \mu w + r(x,t), & x\in \Omega, t>0, \end{array} \right. \end{equation*}$
under homogeneous Neumann boundary conditions in a smoothly bounded domain
$\Omega \subset R^2$
, where the constants
$\mu$
,
$\mu_1$
,
$\mu_2$
,
$\lambda$
,
$m$
and
$l$
are positive. We prove that the corresponding initial-boundary value problem possesses a global classical solution that is uniformly bounded under conditions
$2\leq m < 3$
,
$l \geq 3$
,
$r(x,t) \in C^1(\overline{\Omega}\times[0,\infty))\cup L^{\infty}(\Omega\times(0,\infty))$
and the smooth nonnegative initial functions, which improves the results obtained by Wang and Wang (MMMAS 2020).
Citation: Lu Xu, Chunlai Mu, Qiao Xin. Global boundedness of solutions to the two-dimensional forager-exploiter model with logistic source. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3031-3043. doi: 10.3934/dcds.2020396
##### References:
[1] H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function Spaces, Differential Operators and Nonlinear Analysis, in: Teubner-Texte Math., 133 1993, 9-126. doi: 10.1007/978-3-663-11336-2_1. Google Scholar [2] T. Black, Global generalized solutions to a forager-exploiter model with superlinear degradation and theri eventual regularity properties, Math. Models Methods Appl. Sci., 30 (2020), 1075-1117. doi: 10.1142/S0218202520400072. Google Scholar [3] X. Cao, Global radial renormalized solution to a producer-scrounger model with singular sensitivities, Math. Models Methods Appl. Sci., 6 (2020), 1119-1165. doi: 10.1142/S0218202520400084. Google Scholar [4] H. Chen, J.-M. Li and K. Wang, On the vanishing viscosity limit of a chemotaxis model, Discrete Contin. Dyn. Syst. Ser. A, 40 (2020), 1963-1987. doi: 10.3934/dcds.2020101. Google Scholar [5] A. Friedman, Partial Different Equations, Holt, Rinehart and Winston, New York, 1969. Google Scholar [6] Y. Giga and H. Sohr, Abstrat $L^p$ estimates for the Cauchy problem with aaplications to the Navier-Sotkes equations in exterior domains, J. Funct. Anal., 102 (1991), 72-94. doi: 10.1016/0022-1236(91)90136-S. Google Scholar [7] B. Hu and Y. Tao, To the exclusion of blow-up in three-dimensional chemotaxis-growth model with indirect attractant production, Math. Models Methods Appl. Sci., 26 (2016), 2111-2128. doi: 10.1142/S0218202516400091. Google Scholar [8] C. Jin, Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source, Discrete Contin. Dyn. Syst. Ser. A, 38 (2018), 3547-3566. doi: 10.3934/dcds.2018150. Google Scholar [9] H.-Y. Jin and Z.-A. Wang, Global stabilization of the full attraction-repulsion Keller-Segel system, Discrete Contin. Dyn. Syst. Ser. A, 40 (2020), 3509-3527. doi: 10.3934/dcds.2020027. Google Scholar [10] J. Lankeit and Y. Wang, Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption, Discrete Contin. Dyn. Syst. Ser. A, 37 (2017), 6099-6121. doi: 10.3934/dcds.2017262. Google Scholar [11] H. Li and Y. Tao, Boundedness in a chemotaxis system with indirect signal production and generalized logistic source, Appl. Math. Lett., 77 (2018), 108-113. doi: 10.1016/j.aml.2017.10.006. Google Scholar [12] L. Meng, J. Yuan and X. Zheng, Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion, Discrete Contin. Dyn. Syst. Ser. A, 39 (2019), 3413-3441. doi: 10.3934/dcds.2019141. Google Scholar [13] N. Mizoguchi and P. Souplet, Nondegeneracy of blow-up points for the parabolic Keller-Segel system, Ann. Inst. H. Poincar$\acute{e}$ Anal. Non Lin$\acute{e}$aire, 31 (2014), 851-875. doi: 10.1016/j.anihpc.2013.07.007. Google Scholar [14] C. Mu, L. Wang, P. Zheng and Q. Zhang, Global existence and boundedness of classical solutions to a parabolic-parabolic chemotaxis system, Nonlinear Anal.: Real World Appl., 14 (2013), 1634-1642. doi: 10.1016/j.nonrwa.2012.10.022. Google Scholar [15] N. Tania, B. Vanderlei, J. P. Heath and L. Edelstein-Keshet, Role of social interactions in dunamic patterns of resource pathches and forager aggregation, Proc. Natl. Acad. Sci. USA, 109 (2012), 11228-11233. Google Scholar [16] Y. Tao, Boundedness in a chemotaxis model with oxygen consumption by bacteria, J. Math. Anal. Appl, 381 (2011), 521-529. doi: 10.1016/j.jmaa.2011.02.041. Google Scholar [17] Y. Tao and M. Winkler, Eventual smoothness and stabilization of larege-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant, J. Differential Equations, 252 (2012), 2520-2543. doi: 10.1016/j.jde.2011.07.010. Google Scholar [18] Y. Tao and M. Winkler, Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system, Z. Angew. Math. Phys., 66 (2015), 2555-2573. doi: 10.1007/s00033-015-0541-y. Google Scholar [19] Y. Tao and M. Winkler, Large time behavior in a forager-exploiter model with differnet taxis strategies for two groups in search of food, Math. Models Methods Appl. Sci., 29 (2019), 2151-2182. doi: 10.1142/S021820251950043X. Google Scholar [20] J. Wang and M. Wang, Global bounded solution of the higher-dimensional forager-exploixer modle with/without growth sources, Math. Models Methods Appl. Sci., 30 (2020), 1297-1323. doi: 10.1142/S0218202520500232. Google Scholar [21] H. Wang and Y. Li, Boundedness in prey-taxis system with rotational flux terms, Commun. pur Appl.Anal, 19 (2020), 4839-4851. doi: 10.3934/cpaa.2020214. Google Scholar [22] M. Winkler, Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions, Math. Models Methods Appl. Sci., 29 (2019), 373-418. doi: 10.1142/S021820251950012X. Google Scholar [23] M. Winkler, Aggregation vs.global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), 2889-2950. doi: 10.1016/j.jde.2010.02.008. Google Scholar
show all references
##### References:
[1] H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function Spaces, Differential Operators and Nonlinear Analysis, in: Teubner-Texte Math., 133 1993, 9-126. doi: 10.1007/978-3-663-11336-2_1. Google Scholar [2] T. Black, Global generalized solutions to a forager-exploiter model with superlinear degradation and theri eventual regularity properties, Math. Models Methods Appl. Sci., 30 (2020), 1075-1117. doi: 10.1142/S0218202520400072. Google Scholar [3] X. Cao, Global radial renormalized solution to a producer-scrounger model with singular sensitivities, Math. Models Methods Appl. Sci., 6 (2020), 1119-1165. doi: 10.1142/S0218202520400084. Google Scholar [4] H. Chen, J.-M. Li and K. Wang, On the vanishing viscosity limit of a chemotaxis model, Discrete Contin. Dyn. Syst. Ser. A, 40 (2020), 1963-1987. doi: 10.3934/dcds.2020101. Google Scholar [5] A. Friedman, Partial Different Equations, Holt, Rinehart and Winston, New York, 1969. Google Scholar [6] Y. Giga and H. Sohr, Abstrat $L^p$ estimates for the Cauchy problem with aaplications to the Navier-Sotkes equations in exterior domains, J. Funct. Anal., 102 (1991), 72-94. doi: 10.1016/0022-1236(91)90136-S. Google Scholar [7] B. Hu and Y. Tao, To the exclusion of blow-up in three-dimensional chemotaxis-growth model with indirect attractant production, Math. Models Methods Appl. Sci., 26 (2016), 2111-2128. doi: 10.1142/S0218202516400091. Google Scholar [8] C. Jin, Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source, Discrete Contin. Dyn. Syst. Ser. A, 38 (2018), 3547-3566. doi: 10.3934/dcds.2018150. Google Scholar [9] H.-Y. Jin and Z.-A. Wang, Global stabilization of the full attraction-repulsion Keller-Segel system, Discrete Contin. Dyn. Syst. Ser. A, 40 (2020), 3509-3527. doi: 10.3934/dcds.2020027. Google Scholar [10] J. Lankeit and Y. Wang, Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption, Discrete Contin. Dyn. Syst. Ser. A, 37 (2017), 6099-6121. doi: 10.3934/dcds.2017262. Google Scholar [11] H. Li and Y. Tao, Boundedness in a chemotaxis system with indirect signal production and generalized logistic source, Appl. Math. Lett., 77 (2018), 108-113. doi: 10.1016/j.aml.2017.10.006. Google Scholar [12] L. Meng, J. Yuan and X. Zheng, Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion, Discrete Contin. Dyn. Syst. Ser. A, 39 (2019), 3413-3441. doi: 10.3934/dcds.2019141. Google Scholar [13] N. Mizoguchi and P. Souplet, Nondegeneracy of blow-up points for the parabolic Keller-Segel system, Ann. Inst. H. Poincar$\acute{e}$ Anal. Non Lin$\acute{e}$aire, 31 (2014), 851-875. doi: 10.1016/j.anihpc.2013.07.007. Google Scholar [14] C. Mu, L. Wang, P. Zheng and Q. Zhang, Global existence and boundedness of classical solutions to a parabolic-parabolic chemotaxis system, Nonlinear Anal.: Real World Appl., 14 (2013), 1634-1642. doi: 10.1016/j.nonrwa.2012.10.022. Google Scholar [15] N. Tania, B. Vanderlei, J. P. Heath and L. Edelstein-Keshet, Role of social interactions in dunamic patterns of resource pathches and forager aggregation, Proc. Natl. Acad. Sci. USA, 109 (2012), 11228-11233. Google Scholar [16] Y. Tao, Boundedness in a chemotaxis model with oxygen consumption by bacteria, J. Math. Anal. Appl, 381 (2011), 521-529. doi: 10.1016/j.jmaa.2011.02.041. Google Scholar [17] Y. Tao and M. Winkler, Eventual smoothness and stabilization of larege-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant, J. Differential Equations, 252 (2012), 2520-2543. doi: 10.1016/j.jde.2011.07.010. Google Scholar [18] Y. Tao and M. Winkler, Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system, Z. Angew. Math. Phys., 66 (2015), 2555-2573. doi: 10.1007/s00033-015-0541-y. Google Scholar [19] Y. Tao and M. Winkler, Large time behavior in a forager-exploiter model with differnet taxis strategies for two groups in search of food, Math. Models Methods Appl. Sci., 29 (2019), 2151-2182. doi: 10.1142/S021820251950043X. Google Scholar [20] J. Wang and M. Wang, Global bounded solution of the higher-dimensional forager-exploixer modle with/without growth sources, Math. Models Methods Appl. Sci., 30 (2020), 1297-1323. doi: 10.1142/S0218202520500232. Google Scholar [21] H. Wang and Y. Li, Boundedness in prey-taxis system with rotational flux terms, Commun. pur Appl.Anal, 19 (2020), 4839-4851. doi: 10.3934/cpaa.2020214. Google Scholar [22] M. Winkler, Global generalized solutions to a multi-dimensional doubly tactic resource consumption model accounting for social interactions, Math. Models Methods Appl. Sci., 29 (2019), 373-418. doi: 10.1142/S021820251950012X. Google Scholar [23] M. Winkler, Aggregation vs.global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations, 248 (2010), 2889-2950. doi: 10.1016/j.jde.2010.02.008. Google Scholar
[1] Ling Liu, Jiashan Zheng. Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3357-3377. doi: 10.3934/dcdsb.2018324 [2] Shijie Shi, Zhengrong Liu, Hai-Yang Jin. Boundedness and large time behavior of an attraction-repulsion chemotaxis model with logistic source. Kinetic & Related Models, 2017, 10 (3) : 855-878. doi: 10.3934/krm.2017034 [3] Liangchen Wang, Yuhuan Li, Chunlai Mu. Boundedness in a parabolic-parabolic quasilinear chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 789-802. doi: 10.3934/dcds.2014.34.789 [4] Guoqiang Ren, Bin Liu. Global boundedness of solutions to a chemotaxis-fluid system with singular sensitivity and logistic source. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3843-3883. doi: 10.3934/cpaa.2020170 [5] Pan Zheng, Chunlai Mu, Xuegang Hu. Boundedness and blow-up for a chemotaxis system with generalized volume-filling effect and logistic source. Discrete & Continuous Dynamical Systems, 2015, 35 (5) : 2299-2323. doi: 10.3934/dcds.2015.35.2299 [6] Abelardo Duarte-Rodríguez, Lucas C. F. Ferreira, Élder J. Villamizar-Roa. Global existence for an attraction-repulsion chemotaxis fluid model with logistic source. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 423-447. doi: 10.3934/dcdsb.2018180 [7] Tomomi Yokota, Noriaki Yoshino. Existence of solutions to chemotaxis dynamics with logistic source. Conference Publications, 2015, 2015 (special) : 1125-1133. doi: 10.3934/proc.2015.1125 [8] Ke Lin, Chunlai Mu. Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2233-2260. doi: 10.3934/dcdsb.2017094 [9] Chunhua Jin. Global classical solution and stability to a coupled chemotaxis-fluid model with logistic source. Discrete & Continuous Dynamical Systems, 2018, 38 (7) : 3547-3566. doi: 10.3934/dcds.2018150 [10] Xie Li, Zhaoyin Xiang. Boundedness in quasilinear Keller-Segel equations with nonlinear sensitivity and logistic source. Discrete & Continuous Dynamical Systems, 2015, 35 (8) : 3503-3531. doi: 10.3934/dcds.2015.35.3503 [11] Xiangdong Zhao. Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020334 [12] Jie Zhao. Large time behavior of solution to quasilinear chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 1737-1755. doi: 10.3934/dcds.2020091 [13] Ke Lin, Chunlai Mu. Global dynamics in a fully parabolic chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5025-5046. doi: 10.3934/dcds.2016018 [14] Wenji Zhang, Pengcheng Niu. Asymptotics in a two-species chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems - B, 2021, 26 (8) : 4281-4298. doi: 10.3934/dcdsb.2020288 [15] Tong Li, Jeungeun Park. Traveling waves in a chemotaxis model with logistic growth. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6465-6480. doi: 10.3934/dcdsb.2019147 [16] Rachidi B. Salako, Wenxian Shen. Existence of traveling wave solutions to parabolic-elliptic-elliptic chemotaxis systems with logistic source. Discrete & Continuous Dynamical Systems - S, 2020, 13 (2) : 293-319. doi: 10.3934/dcdss.2020017 [17] Rachidi B. Salako, Wenxian Shen. Spreading speeds and traveling waves of a parabolic-elliptic chemotaxis system with logistic source on $\mathbb{R}^N$. Discrete & Continuous Dynamical Systems, 2017, 37 (12) : 6189-6225. doi: 10.3934/dcds.2017268 [18] Rachidi B. Salako. Traveling waves of a full parabolic attraction-repulsion chemotaxis system with logistic source. Discrete & Continuous Dynamical Systems, 2019, 39 (10) : 5945-5973. doi: 10.3934/dcds.2019260 [19] Hong Yi, Chunlai Mu, Guangyu Xu, Pan Dai. A blow-up result for the chemotaxis system with nonlinear signal production and logistic source. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2537-2559. doi: 10.3934/dcdsb.2020194 [20] Lei Yang, Lianzhang Bao. Numerical study of vanishing and spreading dynamics of chemotaxis systems with logistic source and a free boundary. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1083-1109. doi: 10.3934/dcdsb.2020154
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# current through the smoothing capacitor in bridge rectifier
Can any one tell the reason for the current through the smoothing capacitor to be pulsating in the full bridge rectifier.
I have attached the screenshots of the circuit and the wave form obtained in Multisim.
• Because the voltage is rippling, and $I_C = C\frac{{\rm d}v}{{\rm d}t}$. – The Photon Sep 15 '17 at 3:51
• Diodes act like a voltage comparator switch between input and stored voltage so Ic * t charge area must equal Iavg * t discharge area and is limited by I=delta V/(cap ESR+ diode ESR + source R) so peak/avg current is inverse to % ripple – Tony Stewart Sunnyskyguy EE75 Sep 15 '17 at 3:54
• Did you expect something different? – Dave Tweed Sep 15 '17 at 4:14
• @Prudhvi Ask a good specific question and you'll get better answers. – Voltage Spike Sep 15 '17 at 4:58
• @Dave Tweed, let me know if you have different explanation – Prudhvi Sep 15 '17 at 17:29
The transformer can only supply current to the load while the transformer voltage is above the capacitor voltage. At all other times the capacitor supplies current to the load.
Since all power ultimately has to come from the transformer and the diodes only conduct part of the time then the current pulses will be many times that of the average load current.
Figure 1. The half-wave rectifier version of the waveforms. The green current waveform has been superimposed on the original graph.
See my answer to Interpreting the ripple curve of a half wave rectifier which discuses the same question for a half-wave rectifier.
• This question comes up often ;) But you forgot transformer inductance, which changes the point diodes stop conducting a little bit... – peufeu Sep 15 '17 at 14:16
The diode will only conduct current to the capacitor when the cyclic voltage from the transformer exceeds the voltage remaining on the capacitor. At other times the diode will block and therefore there will be only a leakage flow of current (very small).
Given that most folk want a DC output that is fairly smooth (i.e. the capacitor is large) the voltage on the capacitor causes the diode to be reverse biased most of the time and the diode will only allow current when the cyclic voltage from the transformer is at or near the peak of it's waveform. Thus, the diode ceases to conduct once the voltage from the transformer starts to reduce.
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Extending the library
OpenGR provides a generic base class gr::MatchBase defining the interface for registration algorithms. Assuming you want to add a new registration algorithm, and depending on the genericity you want to provide to the users, you can consider three different scenarios, from the simplest to the most advanced. Scenario 2 is probably describing the most usual case.
### 1. Simple extension without genericity constraint or custom option
In order to write your own registration algorithm, you need to inherit gr::MatchBase, and implement the initialization and processing methods:
namespace gr {
template <typename _TransformVisitor >
class MatchTestSimple : public gr::MatchBase<_TransformVisitor> {
public:
using MatchBaseType = gr::MatchBase<_TransformVisitor>;
using OptionsType = typename MatchBaseType::OptionsType;
using Scalar = typename MatchBaseType::Scalar;
using MatrixType = typename MatchBaseType::MatrixType;
MatchTestSimple (const OptionsType& options, const gr::Utils::Logger& logger)
:MatchBaseType(options, logger) { }
// Initializes the data structures and needed values before the match computation.
// This method is called once the internal state of the Base class as been set.
void Initialize(const std::vector<Point3D>& P,
const std::vector<Point3D>& Q) override { /* ... */}
// Computes an approximation of the best LCP (directional) from Q to P
// and the rigid transformation that realizes it.
// See gr::MatchBase::ComputeTransformation for more details
Scalar ComputeTransformation(const std::vector<Point3D>& P,
std::vector<Point3D>* Q,
Eigen::Ref<MatrixType> transformation,
const Sampler& sampler,
_TransformVisitor& v) override { return 0; }
};
}
### 2. Simple extension with custom options
gr::MatchBase holds a protected field OptionsType options_; that is used to specify parameters sets to the algorithms. In case your algorithm needs to be configured by some parameter values, OptionsType needs to be extended with your own parameter set.
Suppose that MatchTestSimple needs two parameters value and point. First, you need to declare these parameters in a structure:
namespace gr {
template < class Derived, class TBase>
struct MatchTestSimpleOptions : TBase
{
typename TBase::Scalar value;
typename gr::Point3D point;
};
}
Then, you need to extend OptionsType with MatchTestSimpleOptions. Technically, OptionsType is defined as an aggregate () between gr::MatchBase::Options and any other custom extensions passed as template parameter. This is automatically done by inhering gr::MatchBase as follow:
namespace gr {
template <typename _TransformVisitor>
class MatchTestSimple : public gr::MatchBase<_TransformVisitor, MatchTestSimpleOptions> { /* ... */ };
}
Then, the parameter values can be accessed as options_.value and options_.point in MatchTestSimple.
### 3. Generic new matcher type
In case you plan to add a new type of matcher with several implementations, you might need to provide a fully transparent propagation mechanism for the algorithm variants options. The mechanism presented in this section is exactly the one we used to implement gr::CongruentSetExplorationBase, which is inherited by gr::Match3pcs and gr::Match4pcsBase.
template <typename _TransformVisitor,
template < class, class > typename ... OptExts >
class MyCustomMatcherBase : public gr::MatchBase<_TransformVisitor , OptExts ... , MyCustomBaseOptions> { /* ... */ };
}
and one of its child classes implementing the variants
namespace gr {
template <typename _TransformVisitor >
class Variant1 : public MyCustomMatcherBase<_TransformVisitor, Variant1Options> { /* ... */ };
}
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Chapter 56
An understanding of neonatal circulatory pathology is intrinsically linked to an understanding of circulatory adaptation to extrauterine life (see Chapter 43). In the fetal circulation, better oxygenated blood is returned from the placenta to the fetus via the umbilical vein. This blood is streamed by the ductus venosus across the right atrium, through the foramen ovale, and into the left atrium, facilitating delivery of the best oxygenated fetal blood to the brain and upper body. Blood returning via the vena cavae is streamed through the right side of the heart and into the descending aorta via the ductus arteriosus. This blood preferentially streams through the ductus because of arteriolar constriction and the high vascular resistance in the fetal lungs. The right-to-left ductal blood flow supplies the lower part of the body and also returns blood to the placenta via the umbilical arteries, which arise from the iliac arteries.
At birth, this blood flow pattern changes quickly. The lungs expand with the first breaths, the pulmonary arterioles dilate, right heart pressures fall, and blood pours into the pulmonary circulation to collect oxygen. The removal of the low-resistance placenta from the systemic circulation increases resistance and pressure on the left side of the circulation, while the pulmonary blood flow increases the left heart preload. The result is a dramatic increase in the workload of the left heart. The muscle in the wall of the ductus arteriosus constricts in response to rising oxygen levels, closing functionally within the first 24 hours after birth and structurally after several days to become a fibrous band.
During the last trimester, much of the fetal cardiopulmonary development is in preparation for the changes that have to occur at birth. Babies born prematurely have exquisite circulatory vulnerability during this period of the transitional circulation. More mature babies are also vulnerable if born in a compromised condition or if they become unwell shortly after birth.
Poor color, increased heart rate, prolonged capillary refill, and low urinary output suggest circulatory compromise. Blood measurements such as low pH and rising lactate can supplement the clinical assessments. These indicators are useful in identifying the baby with severe circulatory compromise, but they have limited accuracy for babies with lesser degrees of compromise.2
### Blood Pressure
Blood pressure can be accurately measured and continuously monitored if there is intra-arterial vascular access. Because blood pressure is relatively easy to monitor, it has traditionally been the primary indicator of neonatal circulatory status, and much conventional circulatory support has focused on increasing the low blood pressure.3 Strong data exists for the importance of a normal blood pressure range4 (Fig. 56-1), but controversy arises over what constitutes an adequate blood pressure that is, the blood pressure below which organ injury can result.5 Further, an emerging body of evidence questions the accuracy of blood pressure as a gold standard for circulatory well-being.6-8 There ...
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# Formulations for COVID-19 Early Stage Treatment via Silver Nanoparticles Inhalation Delivery at Home and Hospital
Preprint
, 1
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There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
### Abstract
Objectives: For suppressing both viral and bacterial respiratory infections, we investigate the possibility of obtaining real effective minimal inhibitory concentration (MIC) of silver nanoparticles in various respiratory system target locations. Applications include (i) control local outbreaks of COVID-19 via early stage home treatment, and (ii) lower the risk of ventilator associated pneumonia (VAP) in hospital ICU. Our prime objective is to propose a first line intervention measure with the potential to suppress proliferation of the viral infection across the respiratory system, thereby giving more time for proper immune system response and lowering the risk for aggravation and spread of the infection. We further discuss the available credible evidence for human safety consideration, by inhalation delivery, for facilitating immediate clinical trials. In addition, we discuss possible manufacturing and commercial availability of the method elements for near term wide public usage.
Method: Based on previously published experimental data, on the antiviral effectiveness of colloidal silver, we propose a model method and computation for achieving antiviral MIC of silver particles in various respiratory system locations, by: (a) analysing the nanoparticle size dependent required concentration. (b) computing the required aerosol delivery characteristics. In order to compute the require delivery dosage, we take into account deposition fraction losses and also inhalation time fraction of the normal breathing cycle. We evaluate independent targeting of: (i) the trachea-bronchial tree (mucus volume of about 1cc), and (ii) the alveoli (total mucus volume of about 10cc).
Results: The dosage is highly sensitive to the silver nanoparticle size, with 3nm - 7nm being the optimal size. Effective antibacterial MIC 10 μg/ml is estimated, but for more certainty 25 μg/ml is a reasonable target concentration to achieve in the mucus fluid of the respiratory system. In particular, using colloidal silver of 5nm particles, delivering inhalation of standard 5μ diameter droplets aerosol (e.g., using off-the-shelf ultrasonic mesh nebulizers), we assert that sufficient MIC can be achieved with: (i) depositing a total of just 0.25cc of a 100ppm (μg/ml) source concentration in the bronchial tree, and (ii) depositing a total of 1cc of a 250ppm (μg/ml) source concentration in the lungs alveoli. Yet, after accounting for deposition losses and due to the fact that active inhalation time is just about 1/3 of the breathing cycle, we find that that practical effective MIC can be achieved by these aerosolising dosages: (a) for the upper airways and bronchial tree use 2cc of a 100 μg/ml colloidal silver source, while (b) for lungs alveoli delivery use 6cc of a 200 μg/ml colloidal silver source. This would be reduced by a factor 3 if a breath actuated ultrasonic nebulizer is used.
Conclusions: We conclude that effective MIC is achievable, both in the bronchial tree and in the alveoli (though the specific aerosol prescription may differ). Since respiratory infections start most commonly in the upper airways, it would be best to use the presented method early on as a first line treatment to suppress the progression of the infection. The required formulations are presently not available on the market but are easy to mass produce OTC in principle. Using off-the-shelf ultrasonic nebulizers and providable OTC colloidal silver formulations, we posit that our suggested method can be used precautionarily at home by anyone feeling the early signs of a potential infection. In addition, due to the anti-bacterial properties of colloidal silver, our method can serve in hospital intensive care units (ICU) as a new standard of care prophylactic treatment for ventilator acquired pneumonia (VAP).
### Author and article information
###### Journal
ScienceOpen Preprints
ScienceOpen
28 March 2020
###### Affiliations
[1 ] Yamor Technologies Ltd.
###### Article
10.14293/S2199-1006.1.SOR-.PPHBJEO.v1
This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
Respiratory medicine, Pharmacology & Pharmaceutical medicine, Infectious disease & Microbiology
A peer review should focus on the content but here it is necessary to comment on the single author of this preprint. This is his first article or preprint that has anything to do with biology or chemistry. The last article he published dates from more than 15 years ago and deals with theoretical physics. He has no academic affiliation but he is CEO of two companies. The one he uses to sign the article does not seem to have any existence beyond his profile (according to a Google search). The other one, Biovo technologies, develops/sells “groundbreaking medical devices […]” and its “premier product line – Airway Medix – presents a line of disposable respiratory devices used for mechanically ventilated patients.” In spite of this, there is no conflict of interest declaration in the preprint.
The article itself makes the case for starting clinical trials consisting in injecting large amounts of silver nanoparticles by inhalation in Covid-19 patients. There is no preclinical work to support this. The in vitro work, from the literature, is on other viruses, and is of poor quality, often in completely artificial and unrealistic models. There is simply no reliable evidence or efficacy model to support exploring this route. The model – if I can use this word - shown in figure 5 is completely naïve.
In general, and particularly in a time of pandemic, sharing articles that make unsupported recommendations for therapeutic interventions is highly problematic. Whilst preprint servers have a role to play in accelerating the circulation of information, there is also a risk that they contribute to amplify bad science noise (at best) or even cause harm (at worst).
2020-04-22 11:31 UTC
+1
One person recommends this
wrote:
Under the request of the journal editor, the detailed response below is coupled with an updated version of the article (dated 2020/May/28).
The field of colloidal silver (potential) therapy is indeed unfortunately plagued by commercial unscientific claims. The review itself does not provide any substantial technical claims. But we will still treat it seriously and take this opportunity to (i) improve some aspect of the article, (ii) prevent similar superficial reviewing in the future, and (iii) address the noted issues constructively.
1. The reviewer presents my position as CEO of a medical device company as a negative or irrelevant. For removal of any doubt, I will clarify: In the past 10 years I have been the founder and CEO of a medical device company developing hospital intensive care products for prevention of ventilator associated pneumonia (VAP) infection. In this context, I have initiated and designed animal trials, clinical trials, bacterial biofilm analysis, FDA/CE registration of medical products, and exhibited repeatedly at the annual meetings of the American Association for Respiratory Care (AARC). My personal research output in this context was expressed not in journal articles but in published, examined and approved medical device patents (some of which can be viewed on my ResearchGate profile).
2. The reviewers statement “There is simply no reliable evidence or efficacy model to support exploring this route [for starting clinical trials]….” is based on just his personal opinion that “The invitro work, from the literature, is on other viruses, and is of poor quality”. i.e., he criticizes my quoted references as of “poor quality” science. In response, (i) I added new references of work on Corona type viruses which were not in the original version. (ii) My most key references are by (a) H.H Lara & M.J. Yacaman, from University of Texas San Antonio [ref#5,9] ; (b) Dongxi Xiang, from Harvard Medical School [ref#27] ; (c) Chunying Chen, from the National Center for Nanoscience and Technology Beijing [ref#24]. The reviewer throws unsubstantiated dismissive adjectives. If the reviewer has some scientifically based negative statements to make about these references – We will be thankful to receive them and be appreciative of his insights.
3. The reviewer states his expert opinion that “The model …. is completely naïve”. The reviewers academic record does not show knowledge or experience about inhalation drug delivery. Yet, we don`t blame him for being unknowledgeable of the subject. We recognize that antimicrobial inhalation delivery is a very specialized domain which even most pharmacologists are not familiar with (if one is not involved with intensive care pneumonia research or CF treatment). Our model is in line with the cutting edge of inhalation drug delivery modelling, as elaborated particularly in reference [21] of our article. Indeed, in retrospect, we realized the need to explain in more approachable manner the core knowledge and assumptions that go into the model calculations. Hence, in the updated posting of the article, we expanded both the beginning of the “Formulation Calculation” section and the “Achieving IC at Target Airway Surface Liquid” section. We also added a new Figure-1 and two new references [38,39].
4. The reviewer comment that “there is no conflict of interest declaration in the preprint”. In response, in our updated article posting, we added a conflict of interest statement.
5. To end, the reviewer worries about “… in a time of pandemic, ….. make unsupported recommendations for therapeutic interventions is highly problematic… etc…”. To clarify, our article states clearly that its purpose is the planning of clinical trials.
Altogether, we thank the reviewer for stimulating our improved exposition in the updated post of the article.
2020-05-28 14:28 UTC
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# Thread: reconciling 2 or more data sets when data volume is varying and wide
1. ## reconciling 2 or more data sets when data volume is varying and wide
Hello,
I am a real estate researcher by trade. I am doing a report on median and mean home prices
in my town over a comparable time period. i.e.- quarter to quarter and year over year.
My problem is this:
for example, in the 4th Qtr of 2009, there was 35 sales with a median price of $335,500 and a mean price of$343,960.
In Q1 of 2010 there were only 11 sales with a median of $349,900 and a mean of$368,245
My problem is comparing two or more data sets, that have a large delta in the number of sales.
In this instance, 35 versus 11. With a such a low volume of sales in Q1 I would think that the data is more volatile, yes?
Is there a formula or solution to 'normalize' or show the difference in the two data sets
with regard to the wide delta of sales. I think that the median and mean prices can't be compared correctly
using such high differential sets of sales numbers, am I right or way off?
I did perform a mean price comparison using a 'trimmed mean' analysis but I wanted something with more bite...
to show the volatility of the data when volume is erratic and to conclude that the median and mean
can only be reliable when sales volume is close to each data set.
Basically, to breakdown the data and make it reliable and comparative.
any ideas?
2. My suggestions would be to compare data sets of the same seasonal preiod. I.e Qtr 4 2009 with Qtr 4 2010. Otherwise you could be introducing a bias in your analysis. It might be known that a certain time of year i.e. summer has a better clearance rate for properties than in winter. You need to be clear in avoiding such facotrs to influence your conclusions.
If you do want to make some inferences between data sets that have a different sample size (and in your case a very small sample size) you can employ a 2 sample t-test for differences in the mean.
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## Monday, May 16, 2011
### A new low for Indian economic policy
Strange things in the appointments process:
Please note: LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.
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## Simons, Stephen
Compute Distance To:
Author ID: simons.stephen Published as: Simons, S.; Simons, Stephen Homepage: http://web.math.ucsb.edu/~simons/ External Links: MGP · dblp · GND
Documents Indexed: 119 Publications since 1961, including 2 Books 2 Contributions as Editor Co-Authors: 22 Co-Authors with 24 Joint Publications 564 Co-Co-Authors
all top 5
### Co-Authors
92 single-authored 3 Leih, Thomas J. 3 Robertson, James B. 2 Fitzpatrick, S. P. 2 Rode, Gerd 2 Zălinescu, Constantin 1 Akemann, Charles A. 1 Baillon, Jean-Bernard 1 Bauschke, Heinz H. 1 Bellenger, J. C. 1 Boţ, Radu Ioan 1 Bruckner, Andrew M. 1 Bueno, Orestes 1 Coodey, M. 1 Ramos, Yboon García 1 Lin, Bor-Luh 1 Martínez-Legaz, Juan-Enrique 1 Phelps, Robert Ralph 1 Reich, Simeon 1 Ricceri, Biagio 1 Ruiz Galán, Manuel 1 Spuhler, P. 1 Wang, Shawn Xianfu 1 Weiss, Max L.
all top 5
### Serials
10 Journal of Convex Analysis 9 Archiv der Mathematik 7 Journal of Mathematical Analysis and Applications 6 Mathematische Annalen 6 Proceedings of the American Mathematical Society 5 Bulletin of the Australian Mathematical Society 5 Pacific Journal of Mathematics 5 Set-Valued and Variational Analysis 4 Transactions of the American Mathematical Society 4 Bulletin of the Institute of Mathematics. Academia Sinica 4 Set-Valued Analysis 4 Nonlinear Analysis. Theory, Methods & Applications 3 Studia Mathematica 2 Journal of Optimization Theory and Applications 2 Proceedings of the London Mathematical Society. Third Series 2 Acta Mathematica Hungarica 2 Optimization 2 Journal of Nonlinear and Convex Analysis 2 Journal of the London Mathematical Society 2 Lecture Notes in Mathematics 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 The Mathematical Intelligencer 1 The Annals of Probability 1 Canadian Mathematical Bulletin 1 Journal of Combinatorial Theory. Series A 1 Journal of Mathematical Economics 1 Journal of the Mathematical Society of Japan 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Journal of Global Optimization 1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 1 Positivity 1 Proceedings of the Cambridge Philosophical Society 1 Bulletin de la Société Mathématique de France. Supplément. Mémoires 1 Lecture Notes in Pure and Applied Mathematics 1 Nonconvex Optimization and Its Applications 1 Anais da Academia Brasileira de Ciências 1 Journal of Nonlinear and Variational Analysis
all top 5
### Fields
64 Functional analysis (46-XX) 55 Operator theory (47-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 10 Convex and discrete geometry (52-XX) 7 Operations research, mathematical programming (90-XX) 6 Measure and integration (28-XX) 6 General topology (54-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Real functions (26-XX) 2 General and overarching topics; collections (00-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Statistics (62-XX) 1 Numerical analysis (65-XX)
### Citations contained in zbMATH Open
87 Publications have been cited 792 times in 513 Documents Cited by Year
From Hahn–Banach to monotonicity. 2nd expanded ed. Zbl 1131.47050
Simons, Stephen
2008
Minimax monotonicity. Zbl 0922.47047
Simons, Stephen
1998
The sequence spaces $$l(p_ \nu)$$ and $$m(p_ \nu)$$. Zbl 0128.33805
Simons, S.
1965
A convergence theorem with boundary. Zbl 0237.46012
Simons, S.
1972
Fenchel duality, Fitzpatrick functions and maximal monotonicity. Zbl 1073.47051
Simons, S.; Zălinescu, C.
2005
Minimax theorems and their proofs. Zbl 0862.49010
Simons, Stephen
1995
The range of a monotone operator. Zbl 0863.47034
Simons, S.
1996
A new proof for Rockafellar’s characterization of maximal monotone operators. Zbl 1062.47048
Simons, S.; Zalinescu, C.
2004
Extended and sandwich versions of the Hahn-Banach theorem. Zbl 0174.43703
Simons, S.
1968
Three lectures on minimax and monotonicity. Zbl 0917.47046
Simons, Stephen
1998
Unbounded linear monotone operators on nonreflexive Banach spaces. Zbl 1128.47301
Phelps, R. R.; Simons, S.
1998
Banach limits, infinite matrices and sublinear functionals. Zbl 0176.46001
Simons, S.
1969
The Hahn–Banach–Lagrange theorem. Zbl 1128.46004
Simons, S.
2007
Fenchel duality, Fitzpatrick functions and the Kirszbraun–Valentine extension theorem. Zbl 1075.46020
Reich, Simeon; Simons, Stephen
2005
A flexible minimax theorem. Zbl 0818.49007
Simons, S.
1994
Maximinimax, minimax, and antiminimax theorems and a result of R. C. James. Zbl 0237.46013
Simons, S.
1972
Conjugate functions and subdifferentials in non-normed situations for operators with complete graphs. Zbl 0679.49016
Rodrigues, B.; Simons, S.
1988
An upward-downward minimax theorem. Zbl 0717.49008
Simons, S.
1990
The least slope of a convex function and the maximal monotonicity of its subdifferential. Zbl 0795.49016
Simons, S.
1991
Banach SSD spaces and classes of monotone sets. Zbl 1215.46044
Simons, Stephen
2011
Cyclical coincidence of multivalued maps. Zbl 0616.47044
Simons, S.
1986
Minimal sublinear functionals. Zbl 0199.47601
Simons, S.
1970
An existence theorem for quasiconcave functions with applications. Zbl 0616.47045
Simons, S.
1986
A new minimax theorem and a perturbed James’s theorem. Zbl 1041.46002
Ruiz Galán, M.; Simons, S.
2002
An eigenvector proof of Fatou’s lemma for continuous functions. Zbl 0841.26006
Simons, Stephen
1995
A new version of the Hahn-Banach theorem. Zbl 1040.46004
Simons, S.
2003
The conjugates, compositions and marginals of convex functions. Zbl 1005.49012
Fitzpatrick, S. P.; Simons, S.
2001
Boundedness in linear topological spaces. Zbl 0133.06404
Simons, S.
1964
Positive sets and monotone sets. Zbl 1128.47048
Simons, S.
2007
Maximal monotone multifunctions of Brøndsted-Rockafellar type. Zbl 0992.47024
Simons, Stephen
1999
Minimax and variational inequalities. Are they of fixed-point or Hahn- Banach type? Zbl 0475.49018
Simons, S.
1981
A theorem on lattice ordered groups, results of Pták, Namioka and Banach, and a frontended proof of Lebesgue’s theorem. Zbl 0146.04901
Simons, S.
1967
The occasional distributivity of $$\circ$$ over $$^ +_ e$$ and the change of variable formula for conjugate functions. Zbl 0722.46002
Simons, S.
1990
Minimax theorems with staircases. Zbl 0769.49021
Simons, Stephen
1991
Sum theorems for monotone operators and convex functions. Zbl 0901.47034
Simons, S.
1998
Subtangents with controlled slope. Zbl 0836.49009
Simons, S.
1994
On Terkelsen’s minimax theorem. Zbl 0714.49010
Simons, S.
1990
The convex function determined by a multifunction. Zbl 0879.54022
Coodey, M.; Simons, S.
1996
Dualized and scaled Fitzpatrick functions. Zbl 1100.47042
Simons, Stephen
2006
On the pointwise maximum of convex functions. Zbl 0967.46050
Fitzpatrick, S. P.; Simons, S.
2000
On Ptak’s combinatorial lemma. Zbl 0237.46014
Simons, S.
1972
Abstract Kuhn-Tucker theorems. Zbl 0622.49007
Simons, S.
1988
Five kinds of maximal monotonicity. Zbl 1022.47033
Simons, Stephen
2001
Variational inequalities via the Hahn-Banach theorem. Zbl 0388.46001
Simons, S.
1978
Local reflexivity and (p,q)-summing maps. Zbl 0231.46033
Simons, S.
1972
Variational inequalities for functions on convex sets. Zbl 0536.49004
Rodé, G.; Simons, S.
1983
If $$E'$$ has the metric approximation property then so does $$(E,E')$$. Zbl 0238.46013
Simons, S.
1973
On the Dunford-Pettis property and Banach spaces that contain $$c_0$$. Zbl 0294.46010
Simons, Stephen
1975
Stronger maximal monotonicity properties of linear operators. Zbl 0936.47030
Bauschke, H. H.; Simons, S.
1999
The open mapping and closed range theorems. Zbl 0633.46007
Rodrigues, B.; Simons, S.
1989
Noncompact simplices. Zbl 0199.43703
Simons, S.
1970
Ubiquitous subdifferentials, $$r_L$$-density and maximal monotonicity. Zbl 1333.49032
Simons, Stephen; Wang, Xianfu
2015
Subdifferentials are locally maximal monotone. Zbl 0803.47049
Simons, S.
1993
Swimming below icebergs. Zbl 0807.46002
Simons, S.
1994
The Fitzpatrick function and nonreflexive spaces. Zbl 1113.47038
Simons, S.
2006
Linear $$L$$-positive sets and their polar subspaces. Zbl 1283.47006
Simons, S.
2012
SSDB spaces and maximal monotonicity. Zbl 1242.90291
Simons, Stephen
2011
The bornological space associated with $$R^ I$$. Zbl 0106.08701
Simons, S.
1961
The iterated limit condition, a Fubini theorem and weak compactness. Zbl 0155.45601
Simons, S.
1968
“Densities” and maximal monotonicity. Zbl 1372.47062
Simons, Stephen
2016
Subdifferentials of convex functions. Zbl 0877.49009
Simons, S.
1997
Quadrivariate existence theorems and strong representability. Zbl 1244.47045
Simons, Stephen
2011
LC-functions and maximal monotonicity. Zbl 1106.47044
Simons, Stephen
2006
You cannot generalize the minimax theorem too much. Zbl 0749.49008
Simons, S.
1989
Excesses, duality gaps and weak compactness. Zbl 1011.46013
Simons, Stephen
2002
Splitting quasinorms and metric approximation properties. Zbl 0235.47011
Simons, S.; Leih, T. J.
1972
Another general minimax theorem. Zbl 0745.49010
Simons, Stephen
1991
Almost-fixed-point and fixed-point theorems for discrete-valued maps. Zbl 0764.05009
Baillon, Jean-Bernard; Simons, Stephen
1992
Vector lattices and vector measures. Zbl 0396.46001
Simons, S.
1978
A proof that Souslin Souslin $$H\subset\text{Souslin }H$$. Zbl 0145.01301
Simons, S.
1966
Krein’s theorem without sequential convergence. Zbl 0152.32303
Simons, S.
1967
The core and applications to infinite matrices. Zbl 0176.46002
Simons, S.
1969
Quasidense monotone multifunctions. Zbl 06861465
Simons, Stephen
2018
The directional derivatives and the maximal monotonicity of subdifferentials. (Les dérivées directionnelles et la monotonicité maximale des sous-différentiels.) Zbl 0899.49009
Simons, S.
1994
Polar subspaces and automatic maximality. Zbl 06348359
Simons, S.
2014
New results on $$q$$-positivity. Zbl 1334.47053
García Ramos, Y.; Martínez-Legaz, J. E.; Simons, S.
2012
Addendum to “A flexible minimax theorem”. Zbl 0844.49004
Simons, S.
1995
Minimax theory and applications. Proceedings of the workshop, Erice, Italy, September 30–October 6, 1996. Zbl 0892.00041
Ricceri, Biagio
1998
Bootstrapping the Mazur-Orlicz-König theorem and the Hahn-Banach Lagrange theorem. Zbl 1400.46002
Simons, Stephen
2018
Pictures of monotone operators. Zbl 0862.47029
Simons, S.
1996
On a fixed-point theorem of Cellina. Zbl 0637.47031
Simons, Stephen
1986
Critères de faible compacité en termes du théorème du minimax. (Criterion of weak compactness in termes of minimax theorem). Zbl 0221.46002
Simons, Stephen
1971
The asymmetric sandwich theorem. Zbl 1275.46003
Simons, Stephen
2013
Hahn–Banach theorems and maximal monotonicity. Zbl 1105.46004
Simons, S.
2005
$$\Lambda(\alpha)$$-nuclear maps and quasi-$$\Lambda(\alpha)$$-nuclear maps. Zbl 0291.47016
Simons, S.; Spuhler, P.
1971
A new proof of the maximal monotonicity of subdifferentials. Zbl 1168.49019
Simons, S.
2009
Gossez’s skew linear map and its pathological maximally monotone multifunctions. Zbl 1437.47024
Simons, Stephen
2019
Gossez’s skew linear map and its pathological maximally monotone multifunctions. Zbl 1437.47024
Simons, Stephen
2019
Quasidense monotone multifunctions. Zbl 06861465
Simons, Stephen
2018
Bootstrapping the Mazur-Orlicz-König theorem and the Hahn-Banach Lagrange theorem. Zbl 1400.46002
Simons, Stephen
2018
“Densities” and maximal monotonicity. Zbl 1372.47062
Simons, Stephen
2016
Ubiquitous subdifferentials, $$r_L$$-density and maximal monotonicity. Zbl 1333.49032
Simons, Stephen; Wang, Xianfu
2015
Polar subspaces and automatic maximality. Zbl 06348359
Simons, S.
2014
The asymmetric sandwich theorem. Zbl 1275.46003
Simons, Stephen
2013
Linear $$L$$-positive sets and their polar subspaces. Zbl 1283.47006
Simons, S.
2012
New results on $$q$$-positivity. Zbl 1334.47053
García Ramos, Y.; Martínez-Legaz, J. E.; Simons, S.
2012
Banach SSD spaces and classes of monotone sets. Zbl 1215.46044
Simons, Stephen
2011
SSDB spaces and maximal monotonicity. Zbl 1242.90291
Simons, Stephen
2011
Quadrivariate existence theorems and strong representability. Zbl 1244.47045
Simons, Stephen
2011
A new proof of the maximal monotonicity of subdifferentials. Zbl 1168.49019
Simons, S.
2009
From Hahn–Banach to monotonicity. 2nd expanded ed. Zbl 1131.47050
Simons, Stephen
2008
The Hahn–Banach–Lagrange theorem. Zbl 1128.46004
Simons, S.
2007
Positive sets and monotone sets. Zbl 1128.47048
Simons, S.
2007
Dualized and scaled Fitzpatrick functions. Zbl 1100.47042
Simons, Stephen
2006
The Fitzpatrick function and nonreflexive spaces. Zbl 1113.47038
Simons, S.
2006
LC-functions and maximal monotonicity. Zbl 1106.47044
Simons, Stephen
2006
Fenchel duality, Fitzpatrick functions and maximal monotonicity. Zbl 1073.47051
Simons, S.; Zălinescu, C.
2005
Fenchel duality, Fitzpatrick functions and the Kirszbraun–Valentine extension theorem. Zbl 1075.46020
Reich, Simeon; Simons, Stephen
2005
Hahn–Banach theorems and maximal monotonicity. Zbl 1105.46004
Simons, S.
2005
A new proof for Rockafellar’s characterization of maximal monotone operators. Zbl 1062.47048
Simons, S.; Zalinescu, C.
2004
A new version of the Hahn-Banach theorem. Zbl 1040.46004
Simons, S.
2003
A new minimax theorem and a perturbed James’s theorem. Zbl 1041.46002
Ruiz Galán, M.; Simons, S.
2002
Excesses, duality gaps and weak compactness. Zbl 1011.46013
Simons, Stephen
2002
The conjugates, compositions and marginals of convex functions. Zbl 1005.49012
Fitzpatrick, S. P.; Simons, S.
2001
Five kinds of maximal monotonicity. Zbl 1022.47033
Simons, Stephen
2001
On the pointwise maximum of convex functions. Zbl 0967.46050
Fitzpatrick, S. P.; Simons, S.
2000
Maximal monotone multifunctions of Brøndsted-Rockafellar type. Zbl 0992.47024
Simons, Stephen
1999
Stronger maximal monotonicity properties of linear operators. Zbl 0936.47030
Bauschke, H. H.; Simons, S.
1999
Minimax monotonicity. Zbl 0922.47047
Simons, Stephen
1998
Three lectures on minimax and monotonicity. Zbl 0917.47046
Simons, Stephen
1998
Unbounded linear monotone operators on nonreflexive Banach spaces. Zbl 1128.47301
Phelps, R. R.; Simons, S.
1998
Sum theorems for monotone operators and convex functions. Zbl 0901.47034
Simons, S.
1998
Minimax theory and applications. Proceedings of the workshop, Erice, Italy, September 30–October 6, 1996. Zbl 0892.00041
Ricceri, Biagio
1998
Subdifferentials of convex functions. Zbl 0877.49009
Simons, S.
1997
The range of a monotone operator. Zbl 0863.47034
Simons, S.
1996
The convex function determined by a multifunction. Zbl 0879.54022
Coodey, M.; Simons, S.
1996
Pictures of monotone operators. Zbl 0862.47029
Simons, S.
1996
Minimax theorems and their proofs. Zbl 0862.49010
Simons, Stephen
1995
An eigenvector proof of Fatou’s lemma for continuous functions. Zbl 0841.26006
Simons, Stephen
1995
Addendum to “A flexible minimax theorem”. Zbl 0844.49004
Simons, S.
1995
A flexible minimax theorem. Zbl 0818.49007
Simons, S.
1994
Subtangents with controlled slope. Zbl 0836.49009
Simons, S.
1994
Swimming below icebergs. Zbl 0807.46002
Simons, S.
1994
The directional derivatives and the maximal monotonicity of subdifferentials. (Les dérivées directionnelles et la monotonicité maximale des sous-différentiels.) Zbl 0899.49009
Simons, S.
1994
Subdifferentials are locally maximal monotone. Zbl 0803.47049
Simons, S.
1993
Almost-fixed-point and fixed-point theorems for discrete-valued maps. Zbl 0764.05009
Baillon, Jean-Bernard; Simons, Stephen
1992
The least slope of a convex function and the maximal monotonicity of its subdifferential. Zbl 0795.49016
Simons, S.
1991
Minimax theorems with staircases. Zbl 0769.49021
Simons, Stephen
1991
Another general minimax theorem. Zbl 0745.49010
Simons, Stephen
1991
An upward-downward minimax theorem. Zbl 0717.49008
Simons, S.
1990
The occasional distributivity of $$\circ$$ over $$^ +_ e$$ and the change of variable formula for conjugate functions. Zbl 0722.46002
Simons, S.
1990
On Terkelsen’s minimax theorem. Zbl 0714.49010
Simons, S.
1990
The open mapping and closed range theorems. Zbl 0633.46007
Rodrigues, B.; Simons, S.
1989
You cannot generalize the minimax theorem too much. Zbl 0749.49008
Simons, S.
1989
Conjugate functions and subdifferentials in non-normed situations for operators with complete graphs. Zbl 0679.49016
Rodrigues, B.; Simons, S.
1988
Abstract Kuhn-Tucker theorems. Zbl 0622.49007
Simons, S.
1988
Cyclical coincidence of multivalued maps. Zbl 0616.47044
Simons, S.
1986
An existence theorem for quasiconcave functions with applications. Zbl 0616.47045
Simons, S.
1986
On a fixed-point theorem of Cellina. Zbl 0637.47031
Simons, Stephen
1986
Variational inequalities for functions on convex sets. Zbl 0536.49004
Rodé, G.; Simons, S.
1983
Minimax and variational inequalities. Are they of fixed-point or Hahn- Banach type? Zbl 0475.49018
Simons, S.
1981
Variational inequalities via the Hahn-Banach theorem. Zbl 0388.46001
Simons, S.
1978
Vector lattices and vector measures. Zbl 0396.46001
Simons, S.
1978
On the Dunford-Pettis property and Banach spaces that contain $$c_0$$. Zbl 0294.46010
Simons, Stephen
1975
If $$E'$$ has the metric approximation property then so does $$(E,E')$$. Zbl 0238.46013
Simons, S.
1973
A convergence theorem with boundary. Zbl 0237.46012
Simons, S.
1972
Maximinimax, minimax, and antiminimax theorems and a result of R. C. James. Zbl 0237.46013
Simons, S.
1972
On Ptak’s combinatorial lemma. Zbl 0237.46014
Simons, S.
1972
Local reflexivity and (p,q)-summing maps. Zbl 0231.46033
Simons, S.
1972
Splitting quasinorms and metric approximation properties. Zbl 0235.47011
Simons, S.; Leih, T. J.
1972
Critères de faible compacité en termes du théorème du minimax. (Criterion of weak compactness in termes of minimax theorem). Zbl 0221.46002
Simons, Stephen
1971
$$\Lambda(\alpha)$$-nuclear maps and quasi-$$\Lambda(\alpha)$$-nuclear maps. Zbl 0291.47016
Simons, S.; Spuhler, P.
1971
Minimal sublinear functionals. Zbl 0199.47601
Simons, S.
1970
Noncompact simplices. Zbl 0199.43703
Simons, S.
1970
Banach limits, infinite matrices and sublinear functionals. Zbl 0176.46001
Simons, S.
1969
The core and applications to infinite matrices. Zbl 0176.46002
Simons, S.
1969
Extended and sandwich versions of the Hahn-Banach theorem. Zbl 0174.43703
Simons, S.
1968
The iterated limit condition, a Fubini theorem and weak compactness. Zbl 0155.45601
Simons, S.
1968
A theorem on lattice ordered groups, results of Pták, Namioka and Banach, and a frontended proof of Lebesgue’s theorem. Zbl 0146.04901
Simons, S.
1967
Krein’s theorem without sequential convergence. Zbl 0152.32303
Simons, S.
1967
A proof that Souslin Souslin $$H\subset\text{Souslin }H$$. Zbl 0145.01301
Simons, S.
1966
The sequence spaces $$l(p_ \nu)$$ and $$m(p_ \nu)$$. Zbl 0128.33805
Simons, S.
1965
Boundedness in linear topological spaces. Zbl 0133.06404
Simons, S.
1964
The bornological space associated with $$R^ I$$. Zbl 0106.08701
Simons, S.
1961
all top 5
### Cited by 466 Authors
40 Simons, Stephen 34 Bauschke, Heinz H. 29 Boţ, Radu Ioan 28 Wang, Shawn Xianfu 18 Csetnek, Ernö Robert 14 Borwein, Jonathan Michael 14 Yao, Liangjin 12 Ruiz Galán, Manuel 11 Başar, Feyzi 11 Moursi, Walaa M. 10 Penot, Jean-Paul 9 Martínez-Legaz, Juan-Enrique 8 Kindler, Jürgen 8 Zălinescu, Constantin 7 Orihuela, José 7 Voisei, Mircea Dan 7 Yuan, George Xian-Zhi 6 Kassay, Gábor 6 Lassonde, Marc 6 Reich, Simeon 6 Wanka, Gert 5 Hantoute, Abderrahim 5 Malkowsky, Eberhard 5 Moffat, Sarah M. 5 Sun, Chuanfeng 4 Bartz, Sedi 4 Burachik, Regina Sandra 4 Grad, Sorin-Mihai 4 Iusem, Alfredo Noel 4 Jeyakumar, Vaithilingam 4 László, Csaba Szilárd 4 Mohebi, Hossein 4 Montiel López, Pablo 4 Pfitzner, Hermann 4 Spurný, Jiří 4 Svaiter, Benar Fux 4 Théra, Michel A. 4 Tripathy, Binod Chandra 4 Verona, Andrei 4 Verona, Maria Elena 4 Volle, Michel 4 Zagrodny, Dariusz 3 Adly, Samir 3 Alotaibi, Abdullah M. 3 Altay, Bilâl 3 Basarir, Metin 3 Braha, Naim Latif 3 Çakan, Celal 3 Demiriz, Serkan 3 Dinh The Luc 3 Eberhard, Andrew C. 3 Ernst, Emil O. 3 Frenk, Johannes B. G. 3 Ramos, Yboon García 3 Godefroy, Gilles 3 Hazarika, Bipan 3 Hendrich, Christopher 3 Iyahen, S. O. 3 Ji, Shaolin 3 Kartsatos, Athanassios G. 3 Khan, Vakeel A. 3 Kong, Chuiliu 3 König, Heinz 3 Mursaleen, Mohammad 3 Neumann, Michael M. 3 Park, Sehie 3 Raj, Kuldip 3 Rocco, Marco 3 Rode, Gerd 3 Savaré, Giuseppe 3 Taa, Ahmed 2 Adhikari, Dhruba Raj 2 Alduncin, Gonzalo 2 Alimohammady, Mohsen 2 Alwadani, Salihah 2 Ansorena, José Luis 2 Atchonouglo, Kossi 2 Attouch, Hedy 2 Aussel, Didier 2 Bellenger, J. C. 2 Bueno, Orestes 2 Burke, James V. 2 Çakmak, Ahmet Faruk 2 Cascales, Bernardo 2 Chbani, Zaki 2 Cheng, Cao-Zong 2 Combettes, Patrick L. 2 Coodey, M. 2 Correa, Rafael 2 Corvellec, Jean-Noël 2 De Wilde, Marc 2 Delbaen, Freddy 2 Dutta, Salila 2 Fonf, Vladimir P. 2 Fuchssteiner, Benno 2 Hájek, Petr 2 İlkhan, Merve 2 Jules, Florence 2 Kalenda, Ondřej F. K. 2 Kara, Emrah Evren ...and 366 more Authors
all top 5
### Cited in 143 Serials
48 Journal of Mathematical Analysis and Applications 31 Set-Valued and Variational Analysis 26 Journal of Optimization Theory and Applications 22 Proceedings of the American Mathematical Society 20 Mathematical Programming. Series A. Series B 19 Archiv der Mathematik 16 Set-Valued Analysis 14 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Optimization 11 SIAM Journal on Optimization 10 Journal of Functional Analysis 10 Transactions of the American Mathematical Society 9 Mathematische Annalen 9 Journal of Global Optimization 9 Abstract and Applied Analysis 9 Optimization Letters 8 Bulletin of the Australian Mathematical Society 8 Journal of Convex Analysis 8 Nonlinear Analysis. Theory, Methods & Applications 7 Positivity 6 Journal of Approximation Theory 6 Numerical Functional Analysis and Optimization 6 Topology and its Applications 6 Acta Mathematica Hungarica 6 Journal of Inequalities and Applications 5 Israel Journal of Mathematics 4 Czechoslovak Mathematical Journal 4 Glasgow Mathematical Journal 4 Filomat 4 Vietnam Journal of Mathematics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Journal of Soviet Mathematics 3 Manuscripta Mathematica 3 Mathematica Slovaca 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 European Journal of Operational Research 3 Top 3 Acta Mathematica Sinica. English Series 2 Computers & Mathematics with Applications 2 Discrete Mathematics 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Illinois Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of Mathematical Economics 2 Mathematika 2 Quaestiones Mathematicae 2 Semigroup Forum 2 SIAM Journal on Control and Optimization 2 Applied Mathematics and Mechanics. (English Edition) 2 Numerical Algorithms 2 Journal of Elasticity 2 Finance and Stochastics 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 2 Fixed Point Theory and Applications 2 Bulletin de la Société Mathématique de France. Supplément. Mémoires 2 Afrika Matematika 2 Minimax Theory and its Applications 1 American Mathematical Monthly 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 The Mathematical Intelligencer 1 Acta Scientiarum Mathematicarum 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Demonstratio Mathematica 1 Fuzzy Sets and Systems 1 Information Sciences 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Mathematics of Operations Research 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Siberian Mathematical Journal 1 Theoretical Computer Science 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 Statistics & Probability Letters 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Acta Mathematicae Applicatae Sinica. English Series 1 International Journal of Approximate Reasoning 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 The Annals of Applied Probability 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Zeitschrift für Operations Research. Serie A: Theorie 1 Expositiones Mathematicae ...and 43 more Serials
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### Cited in 43 Fields
215 Functional analysis (46-XX) 204 Operator theory (47-XX) 157 Calculus of variations and optimal control; optimization (49-XX) 134 Operations research, mathematical programming (90-XX) 56 Convex and discrete geometry (52-XX) 39 General topology (54-XX) 38 Real functions (26-XX) 36 Sequences, series, summability (40-XX) 27 Numerical analysis (65-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Measure and integration (28-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Ordinary differential equations (34-XX) 6 Partial differential equations (35-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Systems theory; control (93-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of deformable solids (74-XX) 4 Mathematical logic and foundations (03-XX) 4 Combinatorics (05-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Difference and functional equations (39-XX) 4 Probability theory and stochastic processes (60-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Algebraic topology (55-XX) 3 Fluid mechanics (76-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 Associative rings and algebras (16-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)
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# zbMATH — the first resource for mathematics
On stable quadratic polynomials. (English) Zbl 1241.11027
Let $$K$$ be a field. A polynomial $$f\in K[X]$$ is called stable if all its iterates $$f^{(1)}=f, f^{(2)}=f(f),\dots, f^{(n)},\dots$$ are irreducible over $$K$$. The main result of the paper states that almost all irreducible quadratic polynomials in $$\mathbb Z[X]$$ are stable (Theorem 1), but there are no stable quadratic polynomials over a finite field of characteristic $$2$$ (Corollary 11). In the case of finite fields $$\mathbb F_q$$ of odd characteristic it is shown (Theorem 8) that if $$F(X)=g(aX^2+bX+c)$$ is stable and $$\deg g=d$$, then the orbit of $$-b/2a$$ under $$F$$ has $$O(q^{1-\alpha_d})$$ elements with $$\alpha_d=\log 2/2\log(4d)$$.
It was shown by R. Jones and N. Boston [Proc. Am. Math. Soc., 140, No. 6, 1849–1863 (2012; Zbl 1243.11115)] that if $$f(X)=aX^2+bX+c$$ (with $$a\neq 0$$), $$\gamma=-b/2a$$ and the sequence $$-f(\gamma),f^{(2)}(\gamma),\dots,f^{(n)}(\gamma),\dots$$ contains no squares, then $$f$$ is stable. The authors present (Theorem 5) an effective algorithm based on Baker’s method to test whether the assumption of this assertion is satisfied.
##### MSC:
11C08 Polynomials in number theory 11T06 Polynomials over finite fields 37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps
Full Text:
##### References:
[1] Hardy, An introduction to the theory of numbers (1979) · Zbl 0423.10001 [2] DOI: 10.1016/j.ffa.2010.06.005 · Zbl 1222.11143 · doi:10.1016/j.ffa.2010.06.005 [3] DOI: 10.1023/A:1000130114331 · Zbl 0886.11016 · doi:10.1023/A:1000130114331 [4] DOI: 10.1007/BF01974110 · Zbl 0552.10009 · doi:10.1007/BF01974110 [5] Blake, Application of finite fields (1993) · doi:10.1007/978-1-4757-2226-0 [6] Stichtenoth, Algebraic function fields and codes (1993) · Zbl 1155.14022 [7] DOI: 10.1017/S0305004100044418 · doi:10.1017/S0305004100044418 [8] Ayad, Acta Arith. 93 pp 87– (2000) [9] DOI: 10.1112/plms/s3-51.3.385 · Zbl 0622.12011 · doi:10.1112/plms/s3-51.3.385 [10] DOI: 10.4064/aa119-1-4 · Zbl 1088.11078 · doi:10.4064/aa119-1-4 [11] DOI: 10.1112/jlms/jdn034 · Zbl 1193.37144 · doi:10.1112/jlms/jdn034 [12] Jones, Compositio Math. 43 pp 1108– (2007) · Zbl 1166.11040 · doi:10.1112/S0010437X07002667 [13] Iwaniec, Analytic number theory (2004) · doi:10.1090/coll/053 [14] DOI: 10.1090/S0002-9939-10-10404-3 · Zbl 1268.11155 · doi:10.1090/S0002-9939-10-10404-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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# What is the cross product of [-2,0,3] and [1,-1,3] ?
Nov 20, 2016
The vector is =〈3,9,2〉
#### Explanation:
The cross product of 2 vectors is given by the determinant.
$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(d , e , f\right) , \left(g , h , i\right) |$
Where, 〈d,e,f〉 and 〈g,h,i〉 are the 2 vectors.
So, we have,
$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(- 2 , 0 , 3\right) , \left(1 , - 1 , 3\right) |$
$= \hat{i} | \left(0 , 3\right) , \left(- 1 , 3\right) | - \hat{j} | \left(- 2 , 3\right) , \left(1 , 3\right) | + \hat{k} | \left(- 2 , 0\right) , \left(1 , - 1\right) |$
$= \hat{i} \left(3\right) + \hat{j} \left(9\right) + \hat{k} \left(2\right)$
So the vector is 〈3,9,2〉
To verify, we must do the dot products
〈3,9,2〉.〈-2,0,3〉=-6+0+6=0
〈3,9,2〉.〈1,-1,3〉=3-9+6=0
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# CuRio$!ty's question at Yahoo! Answers regarding a linear homogeneous recursion #### MarkFL ##### Administrator Staff member Here is the question: Math help please! recursive formula? consider the sequence defined by the following recursive formula and starting with A^1=3 and A^2=2 A^1=4A^N-1 +A^N-2 A)list the next four terms of the sequence b) find A^g NOTE: ALL SUBSCRIPTS ARE SUPPOSE TO BE LOCATED BELOW THE "A" please show me how this is done. would liketo learn. thanks in advance! I have posted a link there to this topic so the OP can see my work. #### MarkFL ##### Administrator Staff member Hello CuRio\$!ty,
We are (presumably) given the linear homogeneous recursion:
$$\displaystyle A_{n}=4A_{n-1}+A_{n-2}$$
where $$\displaystyle A_1=3,\,A_2=2$$
a) List the next four terms of the sequence.
For this we may simply use the recursive algorithm:
$$\displaystyle A_3=4A_2+A_1=4\cdot2+3=11$$
$$\displaystyle A_4=4A_3+A_2=4\cdot11+2=46$$
$$\displaystyle A_5=4A_4+A_3=4\cdot46+11=195$$
$$\displaystyle A_6=4A_5+A_4=4\cdot195+46=826$$
b) Find $A_n$.
To find the closed form, we find the roots of the associated characteristic equation:
$$\displaystyle r^2-4r-1=0$$
$$\displaystyle r=2\pm\sqrt{5}$$
Hence, the close form is:
$$\displaystyle A_n=c_1\left(2+\sqrt{5} \right)^n+c_2\left(2-\sqrt{5} \right)^n$$
Using the initial values, we may determine the parameters $c_i$:
$$\displaystyle A_1=c_1\left(2+\sqrt{5} \right)+c_2\left(2-\sqrt{5} \right)=3$$
$$\displaystyle A_2=c_1\left(2+\sqrt{5} \right)^2+c_2\left(2-\sqrt{5} \right)^2=2$$
These equations may be written:
$$\displaystyle 2\left(c_1+c_2 \right)+\sqrt{5}\left(c_1-c_2 \right)=3$$
$$\displaystyle 9\left(c_1+c_2 \right)+4\sqrt{5}\left(c_1-c_2 \right)=2$$
Multiplying the first equation by -4 and adding to the second, we obtain:
$$\displaystyle c_1+c_2=-10$$
Multiplying the first equation by 9 and the second by -2 and adding we obtain:
$$\displaystyle c_1-c_2=\frac{23}{\sqrt{5}}$$
Adding together these last two equations, we get:
$$\displaystyle 2c_1=\frac{23}{\sqrt{5}}-10\implies c_1=\frac{23}{2\sqrt{5}}-5$$
and so:
$$\displaystyle c_2=-\left(\frac{23}{2\sqrt{5}}+5 \right)$$
Thus, the closed form for the sequence is:
$$\displaystyle A_n=\left(\frac{23}{2\sqrt{5}}-5 \right)\left(2+\sqrt{5} \right)^n-\left(\frac{23}{2\sqrt{5}}+5 \right)\left(2-\sqrt{5} \right)^n$$
$$\displaystyle A_n=\frac{\sqrt{5}}{10}\left(\left(23-10\sqrt{5} \right)\left(2+\sqrt{5} \right)^n-\left(23+10\sqrt{5} \right)\left(2-\sqrt{5} \right)^n \right)$$
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Resources tagged with Factors and multiples similar to Take Three from Five:
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Broad Topics > Numbers and the Number System > Factors and multiples
Take Three from Five
Stage: 3 and 4 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
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The clues for this Sudoku are the product of the numbers in adjacent squares.
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You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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Stage: 3 Challenge Level:
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
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What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
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Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
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Find the number which has 8 divisors, such that the product of the divisors is 331776.
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Find the highest power of 11 that will divide into 1000! exactly.
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Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
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Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
Factorial
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Factors and Multiples - Secondary Resources
Stage: 3 and 4 Challenge Level:
A collection of resources to support work on Factors and Multiples at Secondary level.
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# Week 2: 09/02/21
Date
Feb 9, 2021 11:15 AM
Event
Tutoring
## Outline of lecture content
### What makes a well posed problem?
• solution exists (for at least as long as the prediction is required)
• the solution is unique
• the solution depends continuously on the initial condition and model parameters
### What is a positively invariant set?
A set $Y \subset X$ is positively invariant if $x(0) \in Y$ implies that $x(t) \in Y$ for all $t \in T$ with $t > 0$. (It is negatively invariant if the same is true for all $t \in T$ with $t < 0$.)
### Stability
• Steady state: $x^*$, is where $f(x^*)=0$
• Stable: for any $\epsilon > 0$ there exists $\delta > 0$ such that $|x(t) − x^*| < \epsilon$ for all positive $t \in T$ whenever $|x_0 − x^*| < \delta$, and unstable otherwise.
• Asymptotically stable: if it is stable and there exists $\delta > 0$ such that $|x− x^*| \rightarrow 0$ as $t → \infty$ whenever $|x_0 − x^*| < \delta$.
• stable: start close, stay close.
• asym. stable: start close, converge to steady state.
### Time dependent solution
If $\frac{dx}{dt}=f(x)$ and $f(x_0)\neq0$, then $$t = \int_{x_0}^{x(t)}\frac{ds}{f(s)}$$
• If $x(t)$ is not a steady state, $x^*$,then it either tends to a steady state or it tends to $\pm\infty$
• If the model system is well-posed, then $x(t)$ must either be a steady state solution, $x^*$, or strictly monotonic.
## Problem sheet 1
The main point of most of this module is to test your abilities to turn a problem often in the form of a paragraph into a mathematical model which you then solve and then learn something about the behaviour of the system or whatever from the solution. Because of this I will not just give you the start of the problem because that is often half of the difficulty in the question. Learning how to do this quickly and effectively now will help you a lot later down the road, so do keep trying even if you feel stuck.
### Question 1
One question you might ask about this problem is why does the dead plant matter have a decreasing number of radioactive carbon atoms but the carbon in the atmosphere does not? This is a bit of a side note but essentially Carbon-14 is produced when particles in the upper atmosphere and troposphere collide with cosmic particles and all sorts of interesting physics happens. These interactions sometimes produce neutrons which can then collide with the abundand nitrogen in the air to make Carbon-14 with the following interaction:
147N + n → 146C + p
Anyway the point is that once the plant dies it is separated from this system of radioactive carbon being created and decaying so we just have the decay. From the lectures we saw that the general radioactive decay equation is $$\dot{x}(t) = -\lambda x(t)$$ which has the solution $$x(t) = x(0)e^{-\lambda t}$$. The key is to figure out what this rate of decay $\lambda$ is in terms of the half-life which we are given. The half-life is the time, $T_{1/2}$ for the amount of 14C to half so we can write that $$\frac{1}{2} = \exp\left[-\lambda T_{1/2}\right]$$ which rearranges to give $$\lambda = \frac{\ln(2)}{T_{1/2}}$$. From here, all we need to do is recognise that we want to find the time $T$ where the activity is $0.97$ and we know that initially the activity was $6.68$ so we have $$0.97 = 6.68 e^{-\lambda T}$$. With some more rearranging we get the solution $$T = \frac{T_{1/2}}{\ln(2)}\ln\left(6.68/0.97\right) \approx 1.5951 \times 10^4 \text{ years}$$
Wondered why the radioactive decay is what it is? It may make intuitive sense to you or it may not. Either way a nice way to think about it is that the probability of a single atom decaying in time $t$ is an exponentially distributed random variable with rate parameter $\lambda$. Over a period of time $t$ the probability that is has not decayed is $1-F(t)=1-e^{-\lambda t}$, where $F(t)$ is the cumulative distribution. If all of the atoms can be treated as independent (and as long as the number of particles is large) then the expected number of particles left by time t is $\langle N\rangle = N_0 e^{-\lambda t}$.
Or we could say that rate of one atom decaying is $\lambda$ so the rate of any of the $N$ particles decaying is $N\lambda$ so this gives us an instantaneous rate of change of the system so $dN=-N\lambda dt$.
I’m sure given some more thought, one of you could make this a bit more rigourous.
### Question 2
Should be relatively straight forward
### Question 3
• a) What do the two terms on the RHS mean physically?
• b) What does the steady state distribution mean for the ODE?
• c) This one is just a following through the maths so I’ll leave that up to you.
### Question 4
This question is pretty straight forwards in terms of setting up the problem. All we need to do is solve the ODE in the case that $c_i=c_a=\text{ constant}$ and substitute in the initial condition that the concentration starts at some value $c_0=c(0)$ so we can substitute this condition in for any constants of integration. Then we do the same for the second case.
The trick in part b is to notice that we can rewrite the ODE as \begin{aligned} c_b'(t) & = \phi \left( c_a \left( \lambda + \phi \alpha (1-\lambda) t \right)- c_b(t)\right) \\\ c_b'(t) + \phi c_b(t) & = \phi\left(c_a\left(\lambda+\phi\alpha(1-\lambda)t\right)\right) \\\ \frac{d}{dt}\left\{c_b(t)e^{\phi t}\right\} & = e^{\phi t}\phi\left(c_a\left(\lambda+\phi\alpha(1-\lambda)t\right)\right) \end{aligned} where we’ve used an integrating factor. From here we can integrate both sides and use integration by parts for the $t\exp[\phi t]$ term.
##### Jeremy Worsfold
###### PhD in Applied Mathematics and Collective Behaviour
My research interests include Collective Behaviour, speficially swarming models and interacting particles Systems. I also have interests in Reinforcement Learning and Scientific Computing.
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# Find Limit of sqrt (8x^2 + 4x - 8) - sqrt (2x^2 - 3x+1) - sqrt (2x^2 + 4x-3) as x->infinity?
## how to rationalize
Mar 8, 2018
$\frac{1}{2 \sqrt{2}}$
#### Explanation:
$\sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} - 3 x + 1} - \sqrt{2 {x}^{2} + 4 x - 3} =$
$\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} - 3 x + 1} + \frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} + 4 x - 3}$
Now
$\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} - 3 x + 1} = \left(\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} - 3 x + 1}\right) \frac{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} - 3 x + 1}}{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} - 3 x + 1}} =$
$= \frac{4 x - 3}{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} - 3 x + 1}}$
and
$\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} + 4 x - 3} = \left(\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} + 4 x - 3}\right) \frac{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} + 4 x - 3}}{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} + 4 x - 3}} =$
$\frac{1 - 3 x}{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} + 4 x - 3}}$
Now
${\lim}_{x \to \infty} \frac{4 x - 3}{\frac{1}{2} \sqrt{8 {x}^{2} + 4 x - 8} + \sqrt{2 {x}^{2} - 3 x + 1}} =$
${\lim}_{x \to \infty} \frac{4 - \frac{3}{x}}{\frac{1}{2} \sqrt{8 + \frac{4}{x} - \frac{8}{x} ^ 2} + \sqrt{2 - \frac{3}{x} + \frac{1}{x} ^ 2}} = \frac{4}{2 \sqrt{2}}$
analogously we can proceed obtaining the final result
${\lim}_{x \to \infty} \sqrt{8 {x}^{2} + 4 x - 8} - \sqrt{2 {x}^{2} - 3 x + 1} - \sqrt{2 {x}^{2} + 4 x - 3} = \frac{1}{2 \sqrt{2}}$
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## Wikipedia - Raggio di Bohr (it) Wikipedia - نصف قطر بور (ar) Bohr radius
https://doi.org/10.1351/goldbook.B00693
Atomic fundamental physical constant used as @[email protected] of length: $a_{0}=\frac{4\ \pi \ \varepsilon_{0}\ \mathrm{\hslash }^{2}}{m_{\text{e}}\ e^{2}}=5.291 \ 772\ 49\ (24)\times 10^{-11}\ \text{m}$ where $$e$$ is the @[email protected], $$\mathrm{\hslash}$$ is the @[email protected] divided by $$2\ \pi$$ and $$m_{\text{e}}$$ is the @[email protected]
Source:
CODATA Bull. 1986, 63, 1 [Terms] [Book]
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# Cyclic components of quotients of abelian varieties mod p
Cristian Virdol
Research output: Contribution to journalArticlepeer-review
## Abstract
Let A an abelian variety of dimension r, defined over Q. For p a rational prime, we denote by Fp the finite field of cardinality p. If A has good reduction at p, let A¯p be the reduction of A at p. Let Γ be a free subgroup of the Mordell–Weil group A(Q), and let Γp be the reduction of Γ at p. In this paper for abelian varieties of type I, II, III, and IV, under Generalized Riemann Hypothesis, Artin's Holomorphy Conjecture, and Pair Correlation Conjecture, we obtain asymptotic formulas for the number of primes p, with p≤x, for which the quotient [Formula presented] has at most 2r−1 cyclic components.
Original language English 135-144 10 Journal of Number Theory 197 https://doi.org/10.1016/j.jnt.2018.08.005 Published - 2019 Apr
## All Science Journal Classification (ASJC) codes
• Algebra and Number Theory
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# Is a phason a Goldstone mode?
This question nagged me for most of Friday. It seems obvious that it is a Goldstone mode. You can translate the ICDW and the energy does not chage. However it is not clear what continuous symmetry remains since the lattice has already broken translation symmetry. To get to the bottom of the issue we should focus on the relevant Hamiltonian which is electron+phonon $$H=\sum_k\epsilon_k c_k^\dagger c_k+\sum_q\hbar\omega_q b_q^\dagger b_q+\sum_{k,q}g(k)c_{k+q}^\dagger c_kb_q+h.c.$$ where $c_k^\dagger$ and $b_q^\dagger$ are electron and phonon creation operators respectively and $h.c.$ denotes Hermitian conjugate of the interaction term. This Hamiltonian is invariant under the continuous transformation $$c_k\to c_k e^{ika\varphi} \\ b_q\to b_q e^{iqa\varphi}$$ for any choice of $\varphi$, and $a$ is the lattice constant. To see this is the relevant phase for CDW consider a simple 1D system with Peierls transition. There the CDW causes phonons to condense and the complex order parameter $\Delta$ is $$\Delta=|\Delta| e^{i\varphi}=g(2k_f)\langle b_{2k_f}+b_{-2k_f}^\dagger\rangle.$$ The phase of $\Delta$ is chosen by spontaneous symmetry breaking with $\varphi$ parameterizing the continuous symmetry so there is a goldstone mode. For completeness the charge density is $$\rho_0+\delta\rho\cos(2k_f x+\varphi).$$ The CDW order parameter I got from this reference.
Upon initial inspection the continuous symmetry here appears to be ordinary translation invariance ($\psi_k\to \psi_k e^{ikr}$). This cannot be correct as translation symmetry was already broken in forming the lattice and phonons. The continuous symmetry that $H$ posses is a $U(1)$ symmetry that is a remnant of the full translation symmetry $\mathbb{R}=\mathbb{Z}\times U(1)$. The $U(1)$ component of $\mathbb{R}$ is a translation symmetry with translation only defined within a unit cell of the lattice. Translation by multiple unit cells comes from the $\mathbb{Z}$ factor of $\mathbb{R}$.
References
I have found multiple references in scientific literature referring to phasons as a Goldstone mode. Below are some examples with links:
• "...the soft, amplitudon and phason (Goldstone) modes..." from Phase Transitions in Liquid Crystals edited by Arthur N. Chester (google book format open to the correct page here)
• " The Goldstone modes evolving from the magnetic satellites consist of transverse spin-wave modes and longitudinal phason modes..." from the abstract of Goldstone Modes and Low-Frequency Dynamics of Incommensurate Chromium Alloys by R.S. Fishman and S.H. Liu (the abstract can be found here)
• "...the strongest mode is the phason (Goldstone) mode..." from Probability Measures on Semigroups: Convolution Products, Random Walks and Random Matrices by Goran Hognas and Arunava Mukherjea (google book format open to the correct page here)
• "...the phason (Goldstone) mode..." from Relaxation Phenomena: Liquid Crystals, Magnetic Systems, Polymers, High-Tc Superconductors, Metallic Glasses edited by Wolfgang Haase (google book format open to the correct page here)
This google search contains more references. This makes it seem like (as tparker stated in the comments) it is "morally" though not strictly a Goldstone mode. This now begs the question, what is the actual relationship between phason/Goldstone modes.
Relationship
After looking around for a more in-depth description of the relationship between phasons and Goldstone modes, I found this physics.SE question. Below the one answer, the second comment says
In my understanding, the Goldstone mode always corresponds to the fluctuation of the "phase" while the fluctuation of "amplitude" may be called Higgs mode. So when we talk about the gapless Goldstone mode in SDW, it should relates to the fluctuation of spin directions rather than spin length. Thus I think there is only "Phason" excitations in SDW, but conventionally we call the excitations "magnons" or spin-wave (classical partner). I hope this comment may be helpful to you.
This paper also has some relevant sections on phasons and Goldstone modes. This book has some information that might be helpful, but unfortunately I cannot find a free copy online and the google book sample I've linked too doesn't include some of the relevant pages.
I also found a quote from the book Liquid Crystals in the Nineties and Beyond (edited by S. Kumar; google book format open to the correct page here) - "The Goldstone mode, which is a phason mode with the wave vector in the center of the dispersion..." which makes it seem like a Goldstone mode is a phason mode, not the other way around.
I found a paper that might also help: Phason dynamics in nonlinear photonic quasicrystals by Barak Freedman, Ron Lifshitz, Jason Fleischer, and Mordechai Segev (the pdf can be downloaded here). The section that seems to be relevant to your Hamiltonian question is on the last page, in the last paragraph...". As such, the observed phason behaviour is representative of a more general hamiltonian dynamics commonly found in non-equilibrium pattern-forming systems". There are, of course, other relevant sections.
Hope this helps! I will continue to update this as I find more information.
Is the existence of a continuous degenerate ground-state manifold more important for "Goldstone-like" behavior than the existence of a continuous spontaneously broken symmetry?
A couple of recent papers by Takahaski and Nitta address this question: https://arxiv.org/pdf/1404.7696v3.pdf
https://arxiv.org/pdf/1410.2391v2.pdf
The authors use Bogoliubov theory to show that when the ground-state exhibits emergent symmetries--i.e. ones which have generators which do not commute with the Hamiltonian--we still anticipate gapless modes arising from the generators of the continuous ground-state degeneracy, called quasi-Goldstone-modes. Essentially, one may identify zero-modes (eigenvectors of $H_{k=0}$ with zero eigenvalue) associated with symmetry generators of the ground-state. However I think this result relies on Bogoliubov theory and is therefore most relevant to Bose-Einstein condensates.
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# How to know here on what variable its a derivative of(diff)
1. Aug 16, 2009
### proto
$$(2x^2ylny-x)y'=y$$
$$(2x^2ylny-x)dy=ydx$$
then i divide both sides by dy
$$(2x^2ylny-x)=yx'$$
then i divide both sides by y
$$(2x^2lny-\frac{x}{y})=x'$$
$$x'+\frac{x}{y}=2x^2lny$$
so i have here a bernuly foruma
i divide both sides by $$x^2$$
$$\frac{x'}{x^2}+\frac{1}{xy}=2lny$$
$$z=x^{-1}$$
$$z'=-1x^{-2}x'$$
$$-z'+\frac{z}{y}=2ln y$$
z is defined to be a function of x
so $$z'=\frac{dz}{dx}$$
why the book interprets $$z'=\frac{dz}{dy}$$
??
z is linked to y not in a direct way .
but z linked to x in a direct way
z and x are more close to each other.
i cant see a mathematical way of figuring it out
its all intuition.and i my intuition is very bad
2. Aug 16, 2009
### Fightfish
$$\frac{dz}{dx} = -\frac{1}{x^2}$$
$$dz = -\frac{1}{x^2} dx$$
$$\frac{dz}{dy} = -\frac{1}{x^2} \frac{dx}{dy}$$
3. Aug 16, 2009
### proto
z=x'
z'=-x^(-2)x'
i cant undestand how you cameup with the first step
$$\frac{dz}{dx} = -\frac{1}{x^2}$$
i cant understand what are you doing here?
4. Aug 16, 2009
### proto
and your conclution
doesnt show that z is a derivative by y
it shows that z' is a derivative by x
5. Aug 16, 2009
### Fightfish
What I was doing up there was proving mathematically that $$\frac{x'}{x^2}$$ necessary equals $$-\frac{dz}{dy}$$. The 1st step was obtained from your substitution variable $$z = x^{-1}$$.
On a more intuitive basis, what are you attempting to do when performing the substitution? It's to simplify the DE via substituting x with a new variable z, and thus why would there be a dx lying around after you have completed your substitution? If $$z' = \frac{dz}{dx}$$, then how are you going to solve $$-z'+\frac{z}{y}=2ln y$$? You now have what, three variables?
6. Aug 16, 2009
### D H
Staff Emeritus
Because you defined it that way, right here:
In the first line you defined z to be a function of x. In the second, you defined z' to be in a derivative of the same variable as used for x' -- which was y.
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# Choosing correct action in bottom up parsing
Using grammar:
$$S \to aABe \\ A \to bcA \mid c \\ B \to b$$
to bottom parse a string $$abcccde$$, the course of action would be: $$\begin{array}{c|c|c|c} \hline Step & Stack & Input & Action \\ \hline 1 & \epsilon & abccde & Shift \\ 2 & a & bccde & Shift \\ 3 & ab & ccde & Shift \\ 4 & abc & cde & Shift \\ 5 & abcc & de & Reduce \, by \, A \to c \\ 6 & abcA & de & Reduce \, by \, A \to bcA \\ 7 & aA & de & Shift \\ 8 & aAd & e & Reduce \, by \, B \to d \\ 9 & aAB & e & Shift \\ 10 & aABe & \epsilon & Reduce \, by \, S \to aABe \\ 11 & S & \epsilon & Done \end{array}$$
My questions are:
1. At step 4, why do we choose to Shift rather than to reduce $$A \to c$$.
2. How would a parser decide which is correct to choose?
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# Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall?
Physicist: This is a beautiful question, in a small part because it’s an interesting thought experiment with some clever math, but mostly because of all the reasons it couldn’t be done and wouldn’t work. Right off the bat; clearly a hole can’t be drilled through the Earth. By the time you’ve gotten no more than 30 miles down (less than 0.4% of the way through) you’ll find your tunnel filling will magma, which tends to gunk up drill bits (also melt everything).
Jumping into a hole drilled through the Earth. What’s the worst that could happen?
But! Assuming that wasn’t an issue, and you’ve got a tube through the Earth (made of unobtainium or something), you still have to contend with the air in the tube. In addition to air-resistance, which on its own would drag you to a stop near the core, just having air in the tube would be really really fatal. The lower you are, the more air is above you, and the higher the pressure. The highest air pressure we see on the surface of the Earth is a little under 16 psi. But keep in mind that we only have about 100 km of real atmosphere above us, and most of that is pretty thin. If the air in the tube were to increase in pressure and temperature the way the atmosphere does, then you’d only have to drop around 50 km before the pressure in the tube was as high as the bottom of the ocean.
Even worse, a big pile of air (like the atmosphere) is hotter at the bottom than at the top (hence all the snow on top of mountains). Temperature varies by about 10°C per km or 30 °F per mile. So, by the time you’ve fallen about 20 miles you’re really on fire a lot. After a few hundred miles (still a long way from the core) you can expect the air to be a ludicrously hot sorta-gas-sorta-fluid, eventually becoming a solid plug.
But! Assuming that there’s no air in the tube, you’re still in trouble. If the Earth is rotating, then in short order you’d be ground against the walls of the tunnel, and would either be pulverized or would slow down and slide to rest near the center of the Earth. This is an effect of “coriolis forces” which show up whenever you try to describe things moving around on spinning things (like planets). To describe it accurately requires the use of angular momentum, but you can picture it pretty well in terms of “higher things move faster”. Because the Earth is turning, how fast you’re moving is proportional to your altitude. Normally this isn’t noticeable. For example, the top of a ten story building is moving about 0.001 mph faster than the ground (ever notice that?), so an object nudged off of the roof can expect to land about 1 millimeter off-target. But over large changes in altitude (and falling through the Earth counts) the effect is very noticeable: about halfway to the center of the Earth you’ll find that you’re moving sideways about 1,500 mph faster than the walls of your tube, which is unhealthy.
The farther from the center you are, the faster you’re moving.
But! Assuming that you’ve got some kind of a super-tube, that the inside of that tube is a vacuum, and that the Earth isn’t turning (and that there’s nothing else to worry about, like building up static electricity or some other unforeseen problem), then you would be free to fall all the way to the far side of the Earth. Once you got there, you would fall right through the Earth again, oscillating back and forth sinusoidally exactly like a bouncing spring or a clock pendulum. It would take you about 42 minutes to make the trip from one side of the Earth to the other.
The clever math behind calculating how an object would fall through the Earth: As you fall all of the layers farther from the center than you cancel out, so you always seem to be falling as though you were on the the surface of a shrinking planet.
What follows is interesting mostly to physics/engineering majors and to almost no one else.
It turns out that spherically symmetric things, which includes things like the Earth, have a cute property: the gravity at any point only depends on the amount of matter below you, and not at all on the amount of matter above you. There are a couple of ways to show this, but since it was done before (with pictures!), take it as read. So, as you fall in all of the layers above you can be ignored (as far as gravity is concerned), and it “feels” as though you’re always falling right next to the surface of a progressively smaller and smaller planet. This, by the way, is just another reason why the exact center of the Earth is in free-fall.
The force of gravity is $F = -\frac{GMm}{r^2}$, where M is the big mass, and m is the smaller, falling mass. But, since you only have to consider the mass below you, then if the Earth has a fixed density (it doesn’t, but if it did) then you could say $M = \rho \frac{4}{3}\pi r^3$, where ρ is the density. So, as you’re falling $F = -\left(\frac{Gm}{r^2}\right)\left(\rho \frac{4}{3}\pi r^3\right) = -\left(\frac{4}{3}G\rho \pi\right) mr$.
Holy crap! This is the (in)famous spring equation, F = – kx! Physicists get very excited when they see this because it’s one of, like, 3 questions that can be exactly answered (seriously). In this case that answer is $r(t) = R\cos{\left(t\sqrt{\frac{4}{3}G\rho \pi} \right)}$, where R is the radius of the Earth, and t is how long you’ve been falling. Cosine, it’s worth pointing out, is sinusoidal.
Interesting fun-fact: the time it takes to oscillate back-and-forth through a planet is dependent only on the density of that planet and not on the size!
This entry was posted in -- By the Physicist, Brain Teaser, Physics. Bookmark the permalink.
### 53 Responses to Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall?
1. alan morriss says:
if the hole was drilled exactly from pole to pole rotational forces would be zero. the difficulties posed by this would be insignificant compared to the rest.
2. In a YouTube video Neil deGrasse Tyson is shown falling through a hypothetical Earth-tunnel:
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### ¿Todavía tienes preguntas de matemáticas?
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Algebra
Pregunta
1. You are required to verify the identity $$\frac { \tan u } { 1 + \tan ^ { 2 } u } = \sin u \cos u .$$ Note that $$1 + \tan ^ { 2 } u = \sec ^ { 2 } u$$ . (This is one of the identities derived from the Pythagorean identity $$\sin ^ { 2 } u + \cos ^ { 2 } u = 1 .$$) Therefore start off as
$$L H S = \frac { \tan u } { 1 + \tan ^ { 2 } u } = \frac { \tan u } { \sec ^ { 2 } u }$$
then complete the verification.
2. You are given that $$u$$ is an angle in quadrant II with $$\sin u = \frac { 5 } { 6 }$$ and $$w$$ is an angle in the fourth quadrant with $$\cos u = \frac { 1 } { 6 }$$ .
(a) Draw $$u$$ and $$w$$ on the axes below then draw a right-angled triangle for $$u$$ and a right-angled triangle for $$w$$ .
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# Integration : Key Stage 5 (AS-Level) : Mathematics Content Knowledge
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# 1. How confident are you that you know and can explain:
## Example
If we are given $\frac{{dy}}{{dx}} = x^2 + 4$ then asked to find y in terms of x, the process by which we do this is called integration.
There is an infinite number of functions that when differentiated give x2 + 4. Three examples are below:
$y = \frac{{x^3 }}{3} + 4x \Rightarrow \frac{{dy}}{{dx}} = x^2 + 4$
$y = \frac{{x^3 }}{3} + 4x + 3 \Rightarrow \frac{{dy}}{{dx}} = x^2 + 4$
$y = \frac{{x^3 }}{3} + 4x - 2 \Rightarrow \frac{{dy}}{{dx}} = x^2 + 4$
So if we are given the gradient function and asked to find the original function, unless we are given additional information we cannot find the original function completely.
So if $\frac{{dy}}{{dx}} = x^2 + 4$ then $y = \frac{{x^3 }}{3} + 4x + c$ where c is the constant of integration.
$y = \frac{{x^3 }}{3} + 4x + c$ is called the integral of $y = x^2 + 4$ with respect to x and is written: $\int {x^2 + 4 \ dx = \frac{{x^3 }}{3} + 4x + c}$.
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# Math Help - find probability mass function
1. ## find probability mass function
The contents of an urn are % blue, 4 red and 6 white balls. Consider the experiment: one chooses a ball from the urn records the color of the ball, puts it back; does this again, then again, then again. Let us assume that one is interested in the number of white balls that were chosen amongst the four balls chosen and let us call the variable "W". Find a probability mass function for "W" where the domain of the function is R( real numbers) and the codomain is R.
2. $f(W=w)=(\frac{6}{15})^w(\frac{9}{15})^{4-w}$
3. typo...there are 5 blue balls
4. How do i know it's summation =1 ? geometric series i would guess?
5. I am sorry to tell you but the first reply is mistaken.
It should be $P(W=n)=\dbinom{4}{n}\left(\dfrac{6}{15}\right)^n \left(\dfrac{9}{15}\right)^{4-n};~n=0,1,2,3,4$
The sum $\sum\limits_{n = 0}^4 {P(W = n)} = 1$ must be true because the total probability mass is 1.
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A ray of light incident at the point (-2,-1) gets reflected from the tangent at (0,-1) to the circle x^2 +y^2 =1 . The reflected ray touches the circle. The equation of the line along which the incident ray moved is ?? Options a) 4x -3y +11=0 b) 4x+3y+11=0 c) 3x +4y+11=0
one year ago
Arun
22576 Points
Let the equation of incident ray be y=m1x c1, and, reflected ray be, y=m2x c2, Equation of tangent to circle at(0,-1), is y=-1, slope 0, now this tangent passes thru (-2,-1), and the ray is incidnt at (-2,-1), Normal at this pt to the tangent is x=-2, slope infinity, now we know, angle of incidnc = angle of reflection, So, Lines y=m1x C1 and y=m2x c2 are equally inclind to normal at (-2,-1) x=-2!! Now using formula for slope,equally inclind lines. (m1-m)/1 m.m1 = (m-m2)/1 m.m2 Where, m=slope of normal x=-2, which is infinity, Solving this, we get, m1 m2 =0! Now since the reflected ray, y=m2x c2, is a tangent to circle, using tangency conditon, (c2)^2 = 1 (m2)^2,.....(1) and also since it passes thru (-2,-1), c2=m2-2!.......(1) Solving(1) and (2) We get, m2=3/4, But we know m1 m2=0,(provd above) So, m1= -3/4; Now since y=m1x c1 also passes thru (-2,-1), Put in equation, we get c1=m1-2 So, c1= -11/4, Now putting c1 and m1 in equation of incident ray, we get, the equation as, 4y 3x 11 =
one year ago
kkbisht
90 Points
The answer is option (b) 4x+3y+11=0Let y=mx+c be the reflected ray touching (tangent) the circle .Using the condition that this reflected ray is tangent if the pependicular drawn from the centre(0,0) of the unit Circle x2 + y2=1 we getc/$\sqrt{}$(1+m2) = 1 => c=$\sqrt{}$(1+m2) therefore the equatio is y=mx+$\sqrt{}$(1+m2). As it passes thogt the point of incidence(-2,-1) we have -1=m(-2) +$\sqrt{}$(1+m2). =>(2m-1)2=1+m2 =>4m2 +1-4m=1+m2 => 3m2-4m=0 => m=0 or m=4/3.Now just see If this tangent makes an angle $\alpha }$ with the normal at the point of incidence.then this tangent will make an angle 90-$\alpha }$ with tanget at the point(0,-1) which is parrale to x-axis.Then by definition slope tan(90-$\alpha }$)=4/3 or cot $\alpha }$= 4/3.Now the incident ray makes an angle 90+$\alpha }$ with the x-axis therefore its slope is tan(90+$\alpha }$)= -cot$\alpha }$= -4/3 ( from above)Hence the equation of the incident ray is y=mx+c passing through (-2,-1) and slope m= -4/3we get after simple calculation the equation as 4x+3y+11=0 kkbisht
one year ago
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# Documentation¶
This is an affiliated package for the AstroPy package. The documentation for this package is here:
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Do not edit this page - instead, place all documentation for the affiliated package inside higal_sedfitter/
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# Mass of Light (photons) at C
## Main Question or Discussion Point
Just a thought, according to Einsteins relativity mass changes with speed and tends to become infnite as it approaches 'c'. Since photons too have mass, why doesnt their mass become infinite since they travel at c?
## Answers and Replies
Related Special and General Relativity News on Phys.org
mathman
Science Advisor
Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c2.
Gyroscope
How is it possible for photons to have momentum if they are massless?
ranger
Gold Member
ranger
Gold Member
robphy
Science Advisor
Homework Helper
Gold Member
Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c2.
Rather than the phrase "rest mass", it might be more appropriate to use the term "invariant mass" or (up to factors of c) "invariant norm of the momentum 4-vector". With this term, then it is easier to see that one can apply the Lorentz Transformation to the photon's [necessarily non-timelike] 4-momentum.
One sees that its square-norm being zero is true in all inertial reference frames. In addition, its temporal component is essentially the relativistic energy (up to constants, the frequency) of the photon. Similar to the "relativistic mass" (or better, up to constants, "relativistic energy"), the relativistic energy of the photon can be boosted toward infinity. (Of course, the "factor" is different... for the photon, it is "k" (the doppler factor), which is $$\gamma(1+v)$$.)
Of course, what you can't do is to boost from the frame of a timelike particle (where that particle is at rest) to one for a null (or lightlike) particle.
Last edited:
jtbell
Mentor
Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c2.
That's not the Lorentz transformation. The Lorentz transformation equations for position and time are
$$x^\prime = \gamma (x - vt)[/itex] [tex]t^\prime = \gamma \left( t - \frac {vx}{c^2} \right)$$
for position and time, and
$$p^\prime = \gamma \left( p - \frac {vE}{c^2}\right)$$
$$E^\prime = \gamma (E - vp)$$
for momentum and energy. As far as I know, they are valid for light (photons) as well as for particles with nonzero "rest mass".
Just a thought, according to Einsteins relativity mass changes with speed and tends to become infnite as it approaches 'c'. Since photons too have mass, why doesnt their mass become infinite since they travel at c?
photon momentum and energy is a frequent topic on the forum. consider a tardyon (u<c) the momentum of which transforms as
p=gp'(1+V/u') (1)
E=gE'(1+Vu'/c^2) (2)
state that special relativity theory ensures a smooth transition from the properties of the tardyon to the properties of a photon and make in (1) and (2) u=u'=c in order to obtain in its case
p(c)=gp'(c)(1+V/c) (3)
E(c)=gE'(c)(1+V/c) (4)
Is there more to say?
sine ira et studio
photon momentum and energy is a frequent topic on the forum. consider a tardyon (u<c) the momentum of which transforms as
p=gp'(1+V/u') (1)
E=gE'(1+Vu'/c^2) (2)
Doesn't look correct. Here are the correct ones.
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html
For the photon you can further simplify the above by using the fact that energy and momentum are related by $$E=c*\sqrt<p,p>$$.
Last edited:
We are not sure that light has zero rest mass or that it travels 100% of the speed of light.
But we do know it is very close to it. Make that very very close.
We are not sure that light has zero rest mass or that it travels 100% of the speed of light.
But we do know it is very close to it. Make that very very close.
Light does not travel at the speed of light? Then why do you call it "the speed of light"?
Is 99.9999999999 equal to 100?
No it isn't, but can you tell? That is the point.
If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the speed of light.
So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?
rbj
Photons have zero "rest mass", so that the Lorentz transformation can't be used - ie. m= (0/0)*c2.
or, looking at it another way, instead of mapping rest mass to "relativistic mass" (or "inertial mass" or whatever it is you get when you divide momentum by velocity),
$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$
map it back the other way:
$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$
so, if the photon has a finite inertial mass
$$E = m c^2 = h \nu$$
or
$$m = \frac{E}{c^2} = \frac{h \nu}{c^2}$$
and the momentum is
$$p = m v = \frac{h \nu}{c^2} v$$
but if the velocity of the photon is $c$, then
$$p = m c = \frac{h \nu}{c}$$
no matter what that finite value is, the rest mass (or "invariant mass") is still zero when $v = c$.
$$m_0 = m \sqrt{1 - \frac{c^2}{c^2}} = m \sqrt{1 - 1} = 0$$
that's my oversimplistic spin on it.
No it isn't, but can you tell? That is the point.
If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the speed of light.
So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?
The speed of light is, well, the speed of light. If you think that photon travel at 0.999999999999c where c is the current value of the speed of light, we can just define the "correct" speed of light as c'=0.999999999999c. :rofl:
pervect
Staff Emeritus
Science Advisor
No it isn't, but can you tell? That is the point.
If a person is accelerated to 99% of the speed of light and that person measures the speed of the photon passing him he will determine the photon is traveling past him at the
of light.
So if two photons are traveling in parallel paths what speed do they measure of each with respect to the other?
Photons don't experience time, and thus they can't measure speed. The closest thing to "experiencing time" is that photon geodesics can be parametrized in terms of an affine parameter, which however is neither like time (timelike) nor like space (spacelike), but null.
There are a number of FAQ's and threads on this
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html
https://www.physicsforums.com/showthread.php?t=132528
and there's a lot more I've skipped over, including one by robphy that was particularly good that I can't find.
You are correct pervect
For this reson if a photon has zero rest mass it may also be an unstable energy unit but without the time to decay for certainly it would have decayed in billions of years of travel if it contained a time component.
As to the light speed.
If a photon has a rest mass particle then it can not attain a speed of C but will only attain a velocity of C ‘ which is slightly less then the theoretical speed of light C.
In this case the measured speed of light is C ’ and the true speed of light C must be calculated or by other means to be known.
The photon must also be a stable energy unit to prevent decay.
rbj
We are not sure that light has zero rest mass or that it travels 100% of the speed of light.
But we do know it is very close to it. Make that very very close.
Light does not travel at the speed of light? Then why do you call it "the speed of light"?
the quantity we call $c$ is the wavespeed of electromagnetic propagation in a vacuum that you get from solving Maxwell's Equations. you know:
$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$
it would be more precise to say that "We are not sure that photons have zero rest mass or that they travel at 100% of the wavespeed of light." BTW, this was something totally new to me a year ago. i still have trouble believing it. (there is the aesthetic part of me that wants the dogma that the speed of photons are $c$ which means they must have zero rest mass.)
Interestingly C was defined by definition in 1983.
Permittivity (E)of free space is defined by C and the Maxwell equations.
Permeability (u) is measured.
Which means C can not be determine by ( or is not determined ?) by the Maxwell equations.
Unless (E) can be measured.
http://en.wikipedia.org/wiki/Speed_of_light
Interestingly C was defined by definition in 1983.
Permittivity (E)of free space is defined by C and the Maxwell equations.
Permeability (u) is measured.
Which means C can not be determine by ( or is not determined ?) by the Maxwell equations.
Unless (E) can be measured.
http://en.wikipedia.org/wiki/Speed_of_light
Correct, as per wiki:
"In metric units, c is exactly 299,792,458 metres per second (1,079,252,848.8 km/h). Note that this speed is a definition, not a measurement. Since the fundamental SI unit of length, the metre, has been defined since October 21, 1983 in terms of the speed of light; one metre is the distance light travels in a vacuum in 1/299,792,458 of a second."
You may wonder why is c defined and not measured to be 299,792,458 metres per second .
The reason is that any physical measurement has certain error attached to it, so that a number had to be chosen. To recap:
1. c is chosen
2. $$\epsilon_0$$ is defined based on c
3.$$\mu_0$$ is derived based on the values chosen at 1 and 2
So, all of the above guarantees that c is exactly 299,792,458
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You may wonder why is c defined and not measured to be 299,792,458 metres per second .
The reason is that any physical measurement has certain error attached to it, so that a number had to be chosen. To recap:
1. c is chosen
2. $$\epsilon_0$$ is defined based on c
3.$$\mu_0$$ is derived based on the values chosen at 1 and 2
So, all of the above guarantees that c is exactly 299,792,458
Actually the reason c is a constant has to do with how the meter is defined.
jtbell
Mentor
It's worth noting that the definitions of SI (MKS) units are made for practical reasons. They are intended to permit the most precise measurements possible, with the current state of technology.
Before 1983, the second was defined in terms of the period of a certain atomic transition, and the meter was defined in terms of the wavelength of another atomic transition. Those definitions were made because they could be reproduced in laboratories with the highest degree of precision possible at the time.
At some point, measurements of the speed of light became intrinsically more precise than the precision of the definition of the meter. Since there was (and still is) no experimental indication that the speed of light is not constant, defining the meter in terms of a constant, defined value of the speed of light maximizes the precision of measurements overall.
If at some point the speed of light is shown not to be constant, then the definition of the meter will surely be changed to reflect this.
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
If at some point the speed of light is shown not to be constant, then the definition of the meter will surely be changed to reflect this.
Actually, that need not necessarily be the case.
A second is defined using the frequency of Cs atoms right now. However, we know that the period of time is frame dependent (i.e. Cs atom in another frame would not have the same frequency). Yet, we still use this as our standard definition of a second.
So based on this, I think we can still use c to define a meter, even if we find (a very big if) situations where it isn't a constant. We just have to clearly define under what conditions this definition is to be used, just like most of our other constants.
Zz.
Interesting thoughts
Because the terms are defined from one another it is impossible to determine if indeed light photons have slightly slower velocity then a theoretical maximum mass speed of light C.
It would be interesting to use the plank constant values to determine the minimum size of a mass particle and accelerate the mass until it had a photon equivalent relativistic mass.
The percentage of the speed of light the photon would achieve could then be calculated.
Different wavelengths would mean different relativistic mass quantities and different velocities however small these velocities differences may be.
It would be interesting to calculate the difference in velocity to determine if the velocity difference is measurable.
The effect would cause different wavelengths from a distant star to reach us with time delays.
Does anyone know if a pulsar has been checked to see if the lower and higher wave lengths are received without a time delay when viewed at the greatest distance possible?
If one photon had one smallest mass particle it would cause a quantum condition because photons could only have a whole number of smallest mass particles.
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Actually the reason c is a constant has to do with how the meter is defined.
c is constant by definition in relativity. In addition, there is ample experimental confirmation, so I don't think that c being a constant has much if anything to do with the meter is defined.
Actually, it is exactly the other way around, the definition of the meter is dependent on c:
http://en.wikipedia.org/wiki/Meter
and on the definition of the second.
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I do not think so.
That is fine, and you seem to be hard to convince , so I won't bother.
For others, the meter is defined in terms of the speed of light. One meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. So obviously c must be 299,792,458.
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# Only show \NAME in \listoftheorems
I am using the thmtools package, and I want to modify \listoftheorems to only print the name of the theorem. For example, my document might look something like the one shown below. When I compile this document, the first line of my "List of Problems" is "1 Problem (Name 1) ... 1". However, I want it to be "1 Name 1 ... 1". Is there anyway to do this? I figured out how to renew the command \listtheoremname in order to change the title of list of problems. The documentation for thmtools says "If you're daring, the code for theorem type "lemma" is in \l@lemma and so on." This makes me optimistic that I can renew the \l@problem command to do what I want, but I don't know enough about TeX to make this happen.
\documentclass{article}
\usepackage{amsthm}
\usepackage{thmtools}
\declaretheorem{problem}
\renewcommand{\listtheoremname}{List of Problems}
\begin{document}
\listoftheorems
\begin{problem}[Name 1]
description of problem 1
\end{problem}
\begin{problem}[Name 2]
description of problem 2
\end{problem}
\end{document}
Try this:
\makeatletter
%\show\ll@problem gives default definition:
% \protect \numberline {\csname the\thmt@envname \endcsname }\thmt@thmname \ifx
% \@empty \thmt@shortoptarg \else \protect \thmtformatoptarg {\thmt@shortoptarg
% }\fi
\def\ll@problem{%
\protect\numberline{\theproblem}\thmt@shortoptarg%
}
\makeatother
it will leave no text if there's no title, but that sounds OK for your case.
• – egreg Dec 16 '13 at 7:53
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# How do I evaluate the indefinite integral intsin^2(2t)dt ?
Jul 28, 2014
$= \frac{1}{2} t - \frac{1}{8} \sin 4 t + c$, where $c$ is a constant
Explanation,
$= \int {\sin}^{2} \left(2 t\right) \mathrm{dt}$
Using trigonometric identity, $\cos 2 t = 1 - 2 {\sin}^{2} t$
${\sin}^{2} t = \frac{1 - \cos 2 t}{2}$, inserting this value of ${\sin}^{2} t$ in integral, we get
$= \int \frac{1 - \cos 4 t}{2} \mathrm{dt}$
$= \frac{1}{2} \int 1 \mathrm{dt} - \frac{1}{2} \int \cos 4 t \mathrm{dt}$
$= \frac{1}{2} t - \frac{1}{2} \frac{\sin 4 t}{4} + c$, where $c$ is a constant
$= \frac{1}{2} t - \frac{1}{8} \sin 4 t + c$, where $c$ is a constant
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# Step-by-step Solution
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## Step-by-step Solution
Problem to solve:
$\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$
Solving method
Learn how to solve quotient of powers problems step by step online.
$\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2y^3\right)^5}$
Learn how to solve quotient of powers problems step by step online. Simplify the quotient of powers (((3x*y^2)^4(2x^3*y^4)^3)^2)/((4x^2*y^3)^5). The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power.
$\frac{6561}{16}y^{25}x^{16}$
$\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$
### Main topic:
Quotient of powers
~ 0.1 s
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## Friday, September 26, 2008 ... //
### Nobel prize winners who didn't sign the letter endorsing Obama
A group of 61 U.S. science Nobel prize winners has signed a somewhat dumb letter endorsing Obama as a visionary leader who will furthermore give more money to science, offer everyone a lot of energy, cure all diseases, and stop the climate from changing. In other words, a true Messiah.
The letter reminds me of some of the "anti-Charter 77" documents supported by scientists and artists who wanted to show how concerned and politically correct they were during communism, by endorsing the only progressive party in the country and by condemning the reactionary elements.
Well, I don't know whether Obama is a visionary. I don't know whether he will give more money to science. And I don't know whether it is a healthy idea to do so. But I am pretty certain that this letter won't mean much.
In democracy, it is a bizarre idea that Nobel prize winners should organize their own political parties and it is a childish idea to think that their Nobel prizes give them a special tool to influence political questions that have nothing to do with their awards.
In the real world, politics and science interact in many ways but there are good reasons to keep them as isolated as possible in many situations. And it is the 61 laureates, and not George Bush - who is squarely in the field of politics, not science - who have transgressed the protective boundaries between science and politics.
And by the way, it would be even more naive to believe that these winners really think that Obama - the famous footnote adviser to Laurence Tribe's crackpot paper called "Curvature of Constitutional Space" - is an intellectual giant above all of the winners as they kindly suggest. :-) They probably have other reasons to write these ludicrous things, don't they?
It might also be interesting to notice that several (alive) U.S. science Nobel prize winners haven't signed it:
• Günter Blobel, medicine
• Baruch Blumberg, medicine
• Paul Boyer, chemistry
• Thomas Čech, chemistry
• Steven Chu, physics
• Elias Corey, chemistry
• Eric Cornell, physics
• Hans Dehmelt, physics
• Gerald Edelman, medicine
• Andrew Fire, medicine
• Robert Furchgott, medicine
• Daniel Gajdusek, medicine
• Murray Gell-Mann, physics
• Ivar Giaever, physics
• Roy Glauber, physics
• Herbert Hauptman, chemistry
• Alan Heeger, chemistry
• David Hubel, medicine
• Russell Hulse, physics
• Jerome Karle, chemistry
• Har Khorana, medicine
• William Knowles, chemistry
• Edwin Krebs, medicine
• Robert Laughlin, physics
• David Lee, physics
• Tsung-Dao Lee, physics
• Yuan Lee, chemistry
• William Lipscomb, chemistry
• Roderick MacKinnon, chemistry
• Rudolph Marcus, chemistry
• John Mather, physics
• Kary Mullis, chemistry
• Joseph Murray, medicine
• George Olah, chemistry
• Arno Penzias, physics
• Martin Perl, physics
• William Phillips, physics
• David Politzer, physics
• Irwin Rose, chemistry
• Andrew Schally, medicine
• John Schriefer, physics
• Phillip Sharp, medicine
• Karl Sharpless, chemistry
• Hideki Shirakawa, chemistry
• Hamilton Smith, medicine
• George Smoot, physics
• Samuel Ting, physics
• Steven Weinberg, physics
• Carl Wieman, physics
• Kenneth Wilson, physics
• Rosalyn Yalow, medicine
• Ahmed Zewail, chemistry
Nothing against the 61 authors of the letter linked above - but thanks to the people in my list. ;-) With 54 non-signatories, we still lost but the results in November can be different.
Among the 54 people, I have spoken to a couple of laureates, including Gell-Mann, Glauber, Hubel, Weinberg, and Wilson. In the list of the pro-Obama signatories, I have talked to Gilbert, Glashow, Gross, Ramsey, and Wilczek, if I haven't forgotten about anyone (which is very likely), so if this filter of mine is included, it's already a tie! :-)
Well, I don't want to claim that e.g. Steven Weinberg will inevitably vote for McCain/Palin but you can't rule out this hypothesis by looking at the letter only! :-) And I am convinced that many people on my list will vote for the GOP ticket and I could even tell you some names if it weren't ... politically incorrect.
Off-topic: Climate Wars, a propagandistic BBC program about the climate science, has led to ... well, Climate Wars: see BBC again.
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# CTAN update: PerlTeX
Date: March 28, 2009 7:30:23 AM CET
This package has been updated at tug.ctan.org and should within a day be at your local mirror. Thanks, Jim Hefferon Saint Michael's College ............................................................................ The following information was provided by our fellow contributor: Name of contribution: PerlTeX Author's name: Scott Pakin Location on CTAN: /macros/latex/contrib/perltex Summary description: Define LaTeX macros in terms of Perl code License type: lppl Announcement text:
PerlTeX is a combination Perl script (perltex.pl) and LaTeX2e style file (perltex.sty) that, together, give the user the ability to define LaTeX macros in terms of Perl code. Once defined, a Perl macro becomes indistinguishable from any other LaTeX macro. PerlTeX thereby combines LaTeX's typesetting power with Perl's programmability. Version 1.8 of PerlTeX adds support for creating documents that can build either with or without PerlTeX. Specifically, the new "optional" package option tells PerlTeX not to issue an error message if Perl is inaccessible, and the new \ifperl macro checks if Perl is accessible, thereby letting the author define fallback macros/environments if it's not.
This package is located at http://tug.ctan.org/tex-archive/macros/latex/contrib/perltex . More information is at http://tug.ctan.org/pkg/perltex (if the package is new it may take a day for that information to appear). We are supported by the TeX Users Group http://www.tug.org . Please join a users group; see http://www.tug.org/usergroups.html .
## perltex – Define LaTeX macros in terms of Perl code
Perl is a combination Perl script (perltex.pl) and package (perltex.sty) that, together, give the user the ability to define macros in terms of Perl code. Once defined, a Perl macro becomes indistinguishable from any other macro. Perl thereby combines 's typesetting power with Perl's programmability. Perl will make use of persistent named pipes, and thereby run more efficiently, on operating systems that offer them (mostly Unix-like systems).
Also provided is a switch to generate a Perl-free, document-specific, noperltex.sty that is useful when distributing a document to places where Perl is not available.
Package perltex Version 2.2 Copyright 2003–2019 Scott Pakin Maintainer Scott Pakin
more
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Lemma 37.59.4. Let $f : X \to S$ be a local complete intersection morphism. Then
1. $f$ is locally of finite presentation,
2. $f$ is pseudo-coherent, and
3. $f$ is perfect.
Proof. Since a perfect morphism is pseudo-coherent (because a perfect ring map is pseudo-coherent) and a pseudo-coherent morphism is locally of finite presentation (because a pseudo-coherent ring map is of finite presentation) it suffices to prove the last statement. Being perfect is a local property, hence we may assume that $f$ factors as $\pi \circ i$ where $\pi$ is smooth and $i$ is a Koszul-regular immersion. A Koszul-regular immersion is perfect, see Lemma 37.58.7. A smooth morphism is perfect as it is flat and locally of finite presentation, see Lemma 37.58.5. Finally a composition of perfect morphisms is perfect, see Lemma 37.58.4. $\square$
There are also:
• 4 comment(s) on Section 37.59: Local complete intersection morphisms
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
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Document Type : Original Manuscript
Author
Department of Mathematics, University of Golestan, P.O. Box ,155 Gorgan, Iran.
Abstract
In this paper we present some inequalities for the order, the exponent, and the number of generators of the polynilpotent multiplier, the Baer invariant with respect to the variety of polynilpotent groups of class row (c_1; · · · ; c_t) of a powerful p-group.Our results extend some of Mashakekhy and Maohammadzadeh’s in 2007 to polynilpotent multipliers.
Keywords
###### ##### References
1. A. J. Bayes, J. Kautsky and J. W. Wamsley, Computation in Nilpotent Groups (application), in : Lecture Notes in Math. 372, Springer-Verlag (1973) 82–89.
2. J. Burns and G. Ellis, On the Nilpotent multipliers of a group, Math. Z., 226 (1997), 405–423.
3. G. Ellis, On the relation between upper central quotients and lower central series of a group, Trans. Amer. Soc., 353 (2001), 4219–4234.
4. M. Hall, The Theory of Groups, MacMillan Company, NewYork, 1959.
5. N. S. Hekster, Varieties of groups and isologisms, J. Austral. Math. Soc., (series A) 46(1) (1989), 22–60.
6. M. R. Jones, Some inequalities for the multiplicator of a finite group, Proc. Amer. Math. Soc., 39 (1973), 450–456.
7. S. Kayvanfar and M. A. Sanati, A bound for the exponent of the Schur multiplier of a some finite p-group, Bull. Iran. Math. Soc., 26(2) (2000), 89–95.
8. A. Lubotzky and A. Mann, Powerful p-groups. I. finite groups, J. Algebra, 105
(1987), 484–505.
9. B. Mashayekhy and M. Parvizi, Polynilpotent multiplier of finitely generated abelian groups, Int. J. Math., Game Theory and Algebra, 16(2) (2006), 93–102.
10. B. Mashayekhy and F. Mohammadzadeh, Some inequalities for nilpotent multipliers of poweful p-groups, Bull. Iran. Math. Soc., 33(2) (2007), 61–71.
11. M. R. R. Moghaddam, Calculation of the Baer invariant of certain groups, Mh. Math., 97 (1984), 191–206.
12. P. Moravec, Schur multipliers and power endomorphisms of groups, J. Algebra,
308 (2007), 12–25.
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# Why is the field inside a capacitor not the sum of the field produced by each plate?
In this answer by David Z, we can read,
When discussing an ideal parallel-plate capacitor, $$\sigma$$ usually denotes the area charge density of the plate as a whole - that is, the total charge on the plate divided by the area of the plate. There is not one $$\sigma$$ for the inside surface and a separate $$\sigma$$ for the outside surface. Or rather, there is, but the $$\sigma$$ used in textbooks takes into account all the charge on both these surfaces, so it is the sum of the two charge densities.
$$\sigma = \frac{Q}{A} = \sigma_\text{inside} + \sigma_\text{outside}$$
With this definition, the equation we get from Gauss's law is
$$E_\text{inside} + E_\text{outside} = \frac{\sigma}{\epsilon_0}$$
where "inside" and "outside" designate the regions on opposite sides of the plate. For an isolated plate, $$E_\text{inside} = E_\text{outside}$$ and thus the electric field is everywhere $$\frac{\sigma}{2\epsilon_0}$$.
Now, if another, oppositely charge plate is brought nearby to form a parallel plate capacitor, the electric field in the outside region (A in the images below) will fall to essentially zero, and that means
$$E_\text{inside} = \frac{\sigma}{\epsilon_0}$$
There are two ways to explain this:
• The simple explanation is that in the outside region, the electric fields from the two plates cancel out. This explanation, which is often presented in introductory textbooks, assumes that the internal structure of the plates can be ignored (i.e. infinitely thin plates) and exploits the principle of superposition.
• The more realistic explanation is that essentially all of the charge on each plate migrates to the inside surface. This charge, of area density $$\sigma$$, is producing an electric field in only one direction, which will accordingly have strength $$\frac{\sigma}{\epsilon_0}$$. But when using this explanation, you do not also superpose the electric field produced by charge on the inside surface of the other plate. Those other charges are the terminators for the same electric field lines produced by the charges on this plate; they're not producing a separate contribution to the electric field of their own.
Either way, it's not true that $$\lim_{d\to 0} E = \frac{2\sigma}{\epsilon_0}$$.
I made the part I couldn't see the reason for in bold.
Let's call the charge density before bringing the other plate $$\sigma$$. The new charge density after bringing the other plate is $$\sigma'=2\sigma$$. Why can't we superimpose the two fields in the second scenario?
If we have a positive charge near a negative one, here too the negative charge acts as a "terminator", yet the total field is the sum of the fields produced by the two charges, not just one.
• IMHO, the quoted explanation is unnecessarily confusing and actually incorrect. I think your intuition in this case is a better guide. – S. McGrew Mar 4 at 17:20
I agree with your assessment. The mistake David makes is assuming that since all of the charge moves to one side of the plate that the field on one side of the plate doubles and the field on the other side goes to $$0$$ due to that plate. Even when the charges all move to one side, the field on each side of the plate is still $$\sigma/2\epsilon_0$$. Then you would still add the two fields together.
The reason the offset of the charges doesn't change anything is because we have assumed infinite sheets of charge so that the field does not depend on the distance from them. Therefore, suggesting that the horizontal translation of charges produces different fields that do not superimpose appears to be incorrect. David's explanation is correct if you have already done the superposition (then you do have $$0$$ field outside and $$\sigma/\epsilon_0$$ inside with field lines starting on positive charges and ending on negative charges).
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# Weak lower semicontinuity of a functional on Hilbert space?
Let $H:=\left\{u\in L^2(R^N):\nabla u \in L^2(R^N)\right\}$ and a functional $$f(u)=\int_{R^N} |\nabla u|^2dx+\left(\int_{R^N} |\nabla u|^2dx\right)^2.$$
If $\{u_n\}\subset H$ is a sequence such that $u_n \rightharpoonup u$, is it true that
$$\liminf_{n\rightarrow +\infty}\left[\int_{R^N} |\nabla u_n|^2dx+\left(\int_{R^N} |\nabla u_n|^2dx\right)^2\right]\geq \int_{R^N} |\nabla u|^2dx+\left(\int_{R^N} |\nabla u|^2dx\right)^2 \;?$$
Given any Hilbert space, if $u_n\rightharpoonup u$ weakly, then $\liminf_{n\to\infty}\|u_n\| \ge \|u\|$.
Proof: W.l.o.g. $\|u\| = 1$. $$\|u\| = \langle u,u \rangle = \lim_{n\to\infty} \langle u,u_n \rangle$$ and $$\langle u,u_n \rangle \le \|u_n\|$$ so $$\lim_{n\to\infty} \langle u,u_n \rangle \le \liminf_{n\to\infty}\|u_n\|$$
I guess the inner product is given by $$\langle u,v\rangle=\int_{\mathbb R^N}u(x)v(x)dx+\sum_{j=1}^N\int_{\mathbb R^N}\dfrac{\partial u}{\partial x_j}(x)\dfrac{\partial v}{\partial x_j}(x)dx.$$ Note that we can find a subsequence $\{u_{n_k}\}$ such that $\lim_{k\to\infty}f(u_{n_k})=\liminf_{n}f(u_n)$, and since the sequence $\{|\nabla u_{n_k}|\}$ and $\{u_{n_k}\}$ are bounded in $L^2(\mathbb R^N)$ , we can extract a subsequence such that $\{u_{\varphi(n)}\}$ and $\{\nabla u_{\varphi(n)}\}$ are weakly convergent in $L^2$. We denote by $v$ and $(v_1,\ldots,v_N)$ these limits. Then weak convergence shows that $\dfrac{\partial v}{\partial x_j}=v_j$, so $u=v$. We can conclude since in an Hilbert space, if a sequence $\{x_n\}$ converges weakly to $x$ then $\lVert x\rVert\leq \liminf_n \lVert x_n\rVert$: \begin{align*} \liminf_n\: f(u_n)&=\lim_{k\to \infty}f(u_{\varphi(k)})\\ &= \liminf_{k\to\infty}\:\left(\int_{\mathbb R^N}|\nabla u_{\varphi(k)}(x)|^2dx+\left(\int_{\mathbb R^N}|\nabla u_{\varphi(k)}(x)|^2dx\right)^2\right)\\ &\geq \liminf_{k\to\infty}\:\int_{\mathbb R^N}|\nabla u_{\varphi(k)}(x)|^2dx+ \left(\liminf_{k\to\infty}\int_{\mathbb R^N}|\nabla u_{\varphi(k)} (x)|^2dx\right)^2\\ &=\int_{\mathbb R^N}|\nabla u(x)|^2dx+\left(\int_{\mathbb R^N}|\nabla u(x)|^2dx\right)^2\\ &=f(u). \end{align*}
• But I cannot see that $u_n\rightharpoonup u$ guarantees finding a subsequence $\{u_{n_k}\}$ such that $lim_{k\rightarrow+\infty} f(u_{n_k})=\liminf_{n\rightarrow} f(u_{n_k} )$. – Jiahua Jin Dec 2 '11 at 9:24
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## ‘Simple’ Isn’t ‘Easy’
You are probably aware that $3^{1/2} = \sqrt{3}$. Sometimes when I’m tutoring I wind up teaching this to young students. Here is the story I use:
You already know that $3^4*3^2 = 3^6$ for a very simple reason.
Forget the reason for a moment, and just focus on the rule. When you multiply exponents with the same base, you can add the powers.
That means
$3^{1/2}*3^{1/2} = 3^1 = 3$
Evidently, $3^{1/2}$ is a number such that if you multiply it by itself, you get three. But that is exactly the meaning of the square root! Hence $3^{1/2} = \sqrt{3}$.
This is a very simple idea, but when I try it on students, it usually fails.
After going through the story, I ask what $16^{1/2}$ is. I’m hoping to hear “four”, but that’s not what happens. Sometimes they say it’s eight. Sometimes they say they don’t know. But the most common response is to go through the whole thing again. The student writes down
$16^{1/2}*16^{1/2} = 16^1 = 16$.
They stare it at for a while. Then they look up at me and say, “Is that right?” We discuss it a bit further to clarify. Circuitously, we stumble upon $16^{1/2}=4$. After that we do a few more half-powers and they get it right. Then I ask what $8^{1/3}$ is. The student will write down
$8^{1/3}*8^{1/3} = 8^{2/3}$.
“It doesn’t work for that one,” they say. “You just get a 2/3 power, and we can’t do that.” So we talk about it some more, until after some time the student can go between roots and exponents.
Then I ask what $4^{3/2}$ is, but they struggle with this, too. Once that’s down we try for $6^{-1}$, but that is also impenetrable (I usually hear that it’s -6). When I suggest trying to figure it out based on the rule of exponent addition, the student feels frustrated and defeated.
It’s curious that I have such difficulty teaching this idea. It is not too complicated or too difficult, even for a young child. It is far simpler than long division and far less abstract than “set the unknown variable equal to x”. The problem is not the sophistication of the idea, but a more fundamental error in communication. When I give my little presentation, the students simply have no idea what I’m doing.
An analogy: I’m teaching someone how to lift weights (this is very hypothetical). I take a dumbbell and I start doing some bicep curls. It’s only a 5-lb dumbbell, and the motion is very simple, so I figure the guy I’m teaching will get it for sure. I hand him the weight and say, “You try.”
When I hand over the weight and the student starts yanking it up and down. He purposely mimics the way I grunt in exertion and copies my facial expressions. He remembers how I looked over my shoulder to talk to him while I demonstrated the exercise, so he looks over his shoulder when trying it out. The weight ultimately does go up and down, but only with a great deal of extraneous commotion. I straighten him out with some effort, but when we move over to the bench press we’ll repeat the whole confused process.
The problem is that before we began, my student didn’t know what weight-lifting is. He didn’t know the point is to make your muscles stronger, or the counter-intuitive idea that to make your muscles stronger, you first have to tire them out by working them hard.
Similarly, my math students watch me do this strange algebraic exercise with exponents not knowing that the goal is to discover new things. They think, instead, that I was simply teaching a new procedure, as in, “This is how you solve problems where the exponent is one half.”
This is not really a big problem. Students can learn new things; that’s what being a student is about. The problem is that students’ ineptitude at this task frustrates me. At times, when watching a student struggle with a problem, I’ve felt ironic wonder at the student’s remarkable creativity – how do they find so many unexpected ways to get everything totally wrong? I wind up concluding that the student is “stupid”, and the student leaves the lesson with only the impression that they have somehow failed at a task they never even understood.
I make these grievous errors in judgment because I assume that since I’ve seen the student handle far more complicated tasks, they should master this one right away. That is not so. ‘Simple’ isn’t ‘easy’. Computing a determinant of a 4×4 matrix isn’t simple, but my students can blaze through it. Showing that the determinant will be zero by noticing that the last row is equal to first row is very simple, but I’ve never had a student use that method.
The things we’re good at are not what’s simplest, but what’s most familiar. The converse also holds: things that are unfamiliar are difficult, even if they’re simple. I personally find it much easier to solve geometry problems using coordinates, algebra, and calculus than using Euclidean geometry, even when the Euclidean approach may be just a few lines of sketching and finding a similar triangle.
When I first noticed that students were having a hard time with problems because they required unfamiliar thinking, and not because they were too hard or because the students were bad, I tried to remedy the situation with speeches. I would talk about how interesting it is to figure out where a formula comes from. I would say over and over that no, I don’t have all the formulas memorized, because as long as I know most of it, I can figure the rest out. I would prove my point by waiting until they embarked on a difficult calculation, and then solving it quickly in my head using some trick or other, supposedly demonstrating how useful it is to be able to approach a problem many different ways. Then I would describe how it’s done. “You’ll like this thing I’m about to show you,” I would say. “It’ll make your life easier.”
This backfired. It mostly led the students to believe that I either gained some ineffable voodoo skills in college or that I am in possession of an extraordinary native intellect that they could never hope to emulate.
I still don’t know quite how to handle the “simple isn’t easy problem”. I have become far more patient when trying to push students’ boundaries, and far less ambitious. I regret the many times I compromised a student’s chance at learning and my own at equanimity by failing to recognize “simple isn’t easy” in practice. I continue to search for simpler and simpler teaching stories, but I don’t spend enough time searching for ways to make the unfamiliar territory easier to navigate. I don’t know how complicated a task that is – to figure out how to build a stepladder to a new level cognition – but I know it isn’t yet easy.
### 4 Responses to “‘Simple’ Isn’t ‘Easy’”
1. Woods Says:
One of the things that I’ve found works well for me in getting students to think “properly” about math is to try to teach almost by virtue of only asking questions, but in a very specific way. I’ll let the student go through a problem, and not say anything until they’re done; while they’re working, I’m only watching and cataloging their mistakes in my head. Then, once they’ve finished, I’ll point out a mistake by asking them a question about something they’ve done in a way that makes a prediction about some other, related, simple problem that they can immediately see the answer to. I’ve found that repeated application of this usually both helps them build up intuition and helps get them in the mindset of looking for ways to check the math that they’re unsure of.
For example, say a student is working on the following problem:
Solve the equation x^2 + 4^2 = 5^2 for x.
One of the common mistakes I see is that students immediately take the square root of both sides incorrectly. e.g., they might work out:
x^2 + 4^2 = 5^2
=> sqrt(x^2 + 4^2) = sqrt(5^2)
=> x + 4 = 5
=> x = 1
Clearly their mistake is that they don’t understand that sqrt(a^2 + b^2) != a + b, so here’s how the following dialog usually goes:
student – “Yeah.”
me – *Pointing at the line in question* “So you’re telling me that sqrt(x^2 + 4^2) = x + 4?”
s – “Yeah.”
me – “So, you would also be telling me that sqrt(2^2 + 2^2) = 2 + 2, right?”
s – “Yeah!”
me – “Is it?”
s – “What do you mean?”
me – “Is the sqrt(2^2 + 2^2) = 2 + 2? That’s simple enough to figure out by hand.”
s – “Oh, ok. Uh… nope.”
me – “Ah hah! So we’ve learned that that’s not how sqrts work! We can’t do that. You better rework the problem.”
And then they’ll go rework the problem, and if there are any mistakes remaining, we’ll go through the questioning process again, and they’ll rework the problem again, and eventually they get it right.
Usually after a few weeks of tutoring, I’ll start to see them checking their math with simple examples whenever they’re not sure how an operation works.
The other specific example where I’ve used this teach-by-questioning tactic often and to great effect is when teaching students what trig functions like sine, cosine, tangent, cosecant, etc look like. That always begins with writing down the unit circle until it’s correct, then I let them draw an entire graph, and there’s lots of questions like:
me – “So you’re telling me that the sin(0) = 1?”
s – “Yeah.”
me – “Sine is the y-part of the coordinates of a point on the unit-circle, right?”
s – “Yeah.”
me – *pointing at (1, 0) on the unit circle* “So you’re telling me that the y-part of this point is 1?”
s – “Yea… oh. Oh! Nnnnooo nonononono. Hang on a minute.” *goes to redraw the graph*
With the trig functions, getting students to correctly draw the graph of tangent is my favorite, because at that time in their math education most of them are very unfamiliar and uncomfortable with the idea of asymptotes, so they almost always draw a continuous graph to start with, so we have lots of fun discussions that start with “So, you’re telling me that somewhere between *here* and *here*, tan(x) = 0?”
2. Salomon Trujillo Says:
So, my mom used to teach algebra at my old high school and it was a small school. (now closed due to the population density gap between the baby boomer’s children and their grandchildren) As a result, her classroom had the full gambit of smart and stupid, lazy and motivated, with every combination of those two spread across five different years of students. All smashed into one class.
Now, my mom is very smart, but she didn’t always think so. She took a math class (I forget if it was algebra or calculus) a bit too young and watched her older brother do well and decided she wasn’t good at math. A few years later, she took it again, initially dreaded it and discovered at it was really easy. Between her own experiences and watching years and years of students take algebra, she came to the conclusion that almost everyone is capable of doing well in algebra, but your brain doesn’t mature to that point until about the age of 13 or so, the variance is quite wide. A student who’s doing poorly in math one year might benefit greatly by simply waiting a year.
On another topic, I recall taking CS1 at Caltech. I’ve been programming since I was a little kid, so I figured CS1 would be a repeat. Well, it was taught in Lisp and it was “Introduction to Computer Science” not “Introductory Programming.” About 90% of was simple and straightforward, learning to program primarily recursively was interesting. But a few things threw me: Big-O notation was one of them. I completely missed the point of the concept at the time (perhaps it was because I skipped lecture, but it’s an example of something that’s very clear to me now and was a mystery to me then.) A year later, I TA’d CS1 and I was talking with the professor as to why we were using Lisp and covering some of the “advanced” topics. He said: “Ever see a terrible program? We’re going to rid the world of bad programs by teaching people how to be computer scientists from the beginning.” In my head, I wondered if he had been taught as a computer scientist from the beginning and if he would have understood encapsulation while he was still trying to master the fundamentals of object-oriented programming.
So, finally, with these two stories in mind, I had a couple questions about your story from above. You ask the kids what 25 ^ 0.5 is, but are they capable of answering “What is the square root of 25″ easily? I recall seeing a half in the exponential and being told: “That’s another way of doing the square root” then verifying it with the exponential arithmetic rule. I will fully agree that the deductive path to figuring it out on the fly is superior and if a child uses it, they will remember it better. But the bread-and-butter aptitude needs to be there in place first. If anything, I would use it as a double-check method, similar to teaching very young children to double-check their subtraction and division problems by relying on their presumably superior addition and multiplication skills, respectively.
Basically, most of these student are just trying to survive their homework and they might not be mature enough. I’ve had some success with getting students to understand the material at a fundamental level, but it has always been under the guise of “this method is easier” and it is easier because it doesn’t require memorization. But it’s always been with material that’s just at the edge of their understanding, and it always used methods that they’re comfortable with.
I guess what I’m trying to say is: don’t feel bad about not pushing your students, they might not be ready yet. They will be.
3. Mark Eichenlaub Says:
Wise advice, Sal. I only have to deal with one student at a time. An entire classroom is an entirely new level of challenge.
I had a similar experience with linear algebra. Only a vague and confused notion of what they were talking about during core, but when I had to go back and learn it for quantum, I picked it up much more easily.
I’m not sure whether struggling with it the first time around and half-comprehending set the stage to understand it the second time, or whether it was mostly other supporting knowledge I picked up in the two intervening years that did the trick, but either way what you mentioned is definitely something I want to keep in mind when I’m tutoring.
4. My Brown Big Spiders « Arcsecond Says:
[...] “Simple” Isn’t “Easy”, I learned not to judge the difficulty of new ideas by how simple they are, but by how familiar to [...]
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# Probability for unknown events
Let A arrive in a party in the time interval [0,a] and B arrive at the same party in the time interval [0,b].
What will be the probability that both of them arrive at the same time ?
Note : Arrival time can be any real number in the interval ,not only integers .
I have no clue what to take as the total number of events or how to approach this problem . Please help .
Zero. Assume that $a < b$ without loss of generality and pick some window of width $d$ in $[0,a]$. B will arrive in that window with probability $\frac{d}{b}$. Simply take the limit as $d \to 0$.
• @user3650050 still zero. The difficulty here is that the "time at which $A$ arrives" is a set of measure zero w.r.t. the standard lebesgue measure. I.e. the "width" of the interval zero. It is like asking "If I pick two real numbers between 0 and 1, what is the probability that I picked the same number both times." While it is not impossible to pick the same number twice in a row, it is so unlikely that we still say that it occurs with probability zero. Afterall, after picking the first number, there is a $\frac{1}{m([0,1])} = \frac{1}{c} \approx 0$ chance of repetition. – JMoravitz Jun 6 '15 at 21:31
• The probability will be positive however if there are a finite number of points of time where $A$ can arrive (i.e. $A$ and $B$ can only arrive at exactly integer multiples of 15 seconds on the clock) or if you allow them to have some sort of nonzero measure (i.e. if you ask "what is the probability that $A$ and $B$ arrive at the party during the same minute?") – JMoravitz Jun 6 '15 at 21:33
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# Maths Formulas for Physics
Maths formulas for physics:
Physics is possible only with the help of mathematics. We need to do a lot of mathematical calculation in Physics.
Mathematics simplifies and helps in solving the problems in physics.
Thus here are some Important mathematics formulas that are needed in physics to solve and simplify any problem:
So Mathematical formulas for physics are:
Geometry:
If Radius of a circle = r then:
it’s circumference = $2 \pi r$
and it’s area = $\pi r^2$
If radius and height of a right circular cylinder are r and h respectively then:
it’s area = $2 \pi r^2 + 2 \pi r h$
And it’s volume = $\pi r^2 h$
Area of a triangle with base “a” and height “h” is : $\dfrac{1}{2} a h$
Mathematical Signs and Symbols:
$=$ :- equals
$\approx$ :- Equals approximately
$\sim$ :- is the order of magnitude of
$\equiv$ :- is identical to , is defined as
$>$ :- is greater than
$\gg$ :- is much greater than
$<$ :- is less than
$\ll$ :- is much less than
$\ge$ :- is greater than or equal to , or is no less than
$\le$ :- is less than or equal to , or is no more than
$\pm$ :- plus or minus
$\propto$ :- is proportional to
$\sum$ :- the sum of
$x_{avg}$ :- the average value of x
if $ax^2 + bx + c =0$ is a quadratic equation
then it’s roots or “x” is: $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Trigonometric Functions of angle $\theta$ :
With reference to the figure following:
trigonometric functions
a> $\sin \theta = \dfrac{y}{r}$ & $\cos \theta = \dfrac{x}{r}$
b> $\tan \theta = \dfrac{y}{x}$ & $\cot \theta = \dfrac{x}{y}$
c> $\sec \theta = \dfrac{r}{x}$ & $\csc \theta = \dfrac{r}{y}$
Trigonometric Identities:
a. $\sin (90 - \theta) = \cos \theta$
b. $\cos (90- \theta) = \sin \theta$
c. $\dfrac{sin \theta}{\cos \theta} = \tan \theta$
d. $\sin ^2 \theta + \cos ^2 \theta = 1$
e. $\sec ^2 \theta - \tan ^2 \theta = 1$
f. $\csc ^2 \theta - \cot ^2 \theta = 1$
g. $\sin 2 \theta = 2 . \sin \theta . \cos \theta$
h. $\cos 2 \theta = \cos ^2 \theta - \sin ^2 \theta = 2 \cos ^2 \theta -1 = 1 - 2 \sin ^2 \theta$
i. $\sin ( \alpha \pm \beta ) = \sin \alpha . \cos \beta \pm \cos \alpha . \sin \beta$
j. $\cos ( \alpha \pm \beta ) = \cos \alpha . \cos \beta \mp \sin \alpha . \sin \beta$
k. $\tan ( \alpha \pm \beta ) = \dfrac{ \tan \alpha \pm \tan \beta }{1 \mp \tan \alpha . \tan \beta}$
l. $\sin \alpha \pm \sin \beta = 2 \sin \frac{1}{2} ( \alpha \pm \beta ) . \cos \frac{1}{2} ( \alpha \mp \beta )$
m. $\cos \alpha + \cos \beta = 2 \cos \frac{1}{2} ( \alpha + \beta ) . \cos \frac{1}{2} ( \alpha - \beta )$
n. $\cos \alpha - \cos \beta = -2 \sin \frac{1}{2} ( \alpha + \beta ) . \sin \frac{1}{2} ( \alpha - \beta )$
Pythagorean theorem:
Referring to the image below:
pythagorean theorem
In the right angled triangle:
$h^2 = p^2 + b^2$
Triangles:
In the following triangle:
triangle
Angles are A , B , C and their corresponding opposite sides are : a , b ,c
Then:
$A + B + C = 180^o$
Sine law:
$\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c}$
Cosine law:
$c^2 = a^2 + b^2 - 2ab \cos c$
, $b^2 = a^2 + c^2 - 2ac \cos b$
& $a^2 = b^2 + c^2 - 2bc \cos a$
Binomial Theorem:
$(1 + x)^n = 1 + \dfrac{nx}{1!} + \dfrac{n(n - 1).x^2}{2!} + \cdots (x^2 < 1)$
Exponential Expansion:
$e^x = 1 + x + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \cdots$
Logarithmic Expansion:
$\ln (1 + x) = x - \frac{1}{2} x^2 + \frac{1}{3} x^3 - \cdots (|x| < 1)$
Trigonometric Expansions:
Note: All $\theta$ are in radians.
a. $\sin \theta = \theta - \dfrac{\theta ^3}{3!} + \dfrac{\theta ^5}{5!} - \cdots$
b. $\cos \theta = 1 - \dfrac{\theta ^2}{2!} + \dfrac{\theta ^4}{4!} - \cdots$
c. $\tan \theta = \theta + \dfrac{\theta ^3}{3!} + \dfrac{2 \theta ^5}{15!} + \cdots$
Cramer’s Rule:
Two simultaneous equations in unknown x and y,
$a_1 x + b_1 y = c_1$ and $a_2 x + b_2 y = c_2$
Have the solutions:
$x = \dfrac{\begin{vmatrix}c_1 & b_1 \\ c_2 & b_2 \end{vmatrix}}{\begin{vmatrix}a_1 & b_1 \\ a_2 & b_2 \end{vmatrix}} = \dfrac{c_1 b_2 - c_2 b_1}{a_1 b_2 - a_2 b_1}$
& $y = \dfrac{\begin{vmatrix}a_1 & c_1 \\ a_2 & c_2 \end{vmatrix}}{\begin{vmatrix}a_1 & b_1 \\ a_2 & b_2 \end{vmatrix}} = \dfrac{a_1 c_2 - a_2 c_1}{a_1 b_2 - a_2 b_1}$
Product of Vectors:
If $\hat{i}$ , $\hat{j}$ & $\hat{k}$ be unit vectors in the x , y and z directions , Then:
$\hat{i} . \hat{i} = \hat{j} . \hat{j} = \hat{k} . \hat{k} = 1$
, $\hat{i} . \hat{j} = \hat{j} . \hat{k} = \hat{k} . \hat{i} = o$
And:
$\hat{i} \times \hat{i} = \hat{j} \times \hat{j} = \hat{k} \times \hat{k} = 0$
& $\hat{i} \times \hat{j} = \hat{k}$ , $\hat{j} \times \hat{k} = \hat{i}$ , $\hat{k} \times \hat{i} = \hat{j}$
If $\theta$ is the smaller angle between two vectors $\overrightarrow{a}$ & $\overrightarrow{b}$ then:
$\overrightarrow{a} . \overrightarrow{b} = a_x b_x + a_y b_y + a_z b_z = ab \cos \theta$
And :
$\overrightarrow{a} \times \overrightarrow{b} = -\overrightarrow{b} \times \overrightarrow{a} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ a_x & a_y & a_z \\ b_x & b_y & b_z \end{vmatrix}$
$= (a_y b_z - a_z b_y) \hat{i} + (a_z b_x - a_x b_z) \hat{j} + (a_x b_y - a_y b_x) \hat{k}$
And $| \overrightarrow{a} \times \overrightarrow{b} | = ab \sin \theta$
Derivatives and Integrals:
The letter “u” & “v” used in formulas following stands for any functions of “x”.
And “a” and “m” are constants.
And it should be noted that although it is not specified in the following formulas , to each indefinite integrals should be added an arbitrary constant of integration.
Derivative formulas:
a. $\dfrac{d}{dx} x = 1$
b. $\dfrac{d}{dx}au = a . \dfrac{d}{dx}u$
c. $\dfrac{d}{dx} (u \pm v) = \dfrac{d}{dx} u \pm \dfrac{d}{dx} v$
d. $\dfrac{d}{dx}x^m = m . x^{m-1}$
e. $\dfrac{d}{dx} \ln x = \dfrac{1}{x}$
f. $\dfrac{d}{dx} (u.v) = v . \dfrac{d}{dx} u + u . \dfrac{d}{dx} v$
g. $\dfrac{d}{dx} e^x = e^x$
h. $\dfrac{d}{dx} \sin x = \cos x$
i. $\dfrac{d}{dx} \cos x = - \sin x$
j. $\dfrac{d}{dx} \tan x = \sec ^2 x$
k. $\dfrac{d}{dx} \sec x = \sec x . \tan x$
l. $\dfrac{d}{dx} \cot x = - \csc ^2 x$
m. $\dfrac{d}{dx} \csc x = - \csc x . \cot x$
n. $\dfrac{d}{dx} e^u = e^u . \dfrac{d}{dx} u$
o. $\dfrac{d}{dx} \sin u = \cos u . \dfrac{d}{dx} u$
p. $\dfrac{d}{dx} \cos u = - \sin u . \dfrac{d}{dx} u$
Integral formulas:
a. $\int dx = x$
b. $\int au dx = a \int u dx$
c. $\int (u + v) dx = \int u dx + \int v dx$
d. $\int x^m dx = \dfrac{x^{m+1}}{m+1} (m \neq -1)$
e. $\int \frac{dx}{x} = \ln |x|$
f. $\int u \frac{dv}{dx} . dx = \int u . dv = uv - \int v . du$
g. $\int e^x dx = e^x$
h. $\int \sin x . dx = - \cos x$
i. $\int \cos x . dx = \sin x$
j. $\int \tan x . dx = \ln | \sec x |$
k. $\int \sin ^2 x . dx = \frac{1}{2} x - \frac{1}{4} \sin 2x$
k. $\int e^{-ax} . dx = - \frac{1}{a} e^{-ax}$
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2. Integration Formulas Using Integration formulas is one of the most basic and...
3. Integration by trigonometric substitution integration by trigonometric substitution: One of the most powerful techniques...
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# zbMATH — the first resource for mathematics
## Freedman, Michael Hartley
Compute Distance To:
Author ID: freedman.michael-hartley Published as: Freedman, M.; Freedman, M. H.; Freedman, Michael; Freedman, Michael H.; Freedman, Michael Hartley Homepage: http://stationq.cnsi.ucsb.edu/~freedman/ External Links: MGP · Wikidata · Celebratio Mathematica · dblp · GND · MacTutor Awards: Fields Medal (1986)
Documents Indexed: 109 Publications since 1975, including 2 Books Biographic References: 2 Publications
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#### Co-Authors
39 single-authored 14 Wang, Zhenghan 7 He, Zheng-Xu 7 Nayak, Chetan 7 Walker, Kevin 6 Krushkal, Vyacheslav S. 4 Kitaev, Alexei Yu. 3 Larsen, Michael Jeffrey 3 Luo, Feng 3 Quinn, Frank S. 3 Teichner, Peter 2 Bonderson, Parsa 2 Calegari, Danny 2 Cui, Shawn X. 2 Demichelis, Stefano 2 Hass, Joel 2 Lovász, László 2 Meyer, David A. 2 Scott, G. Peter 2 Skora, Richard K. 2 Stong, Richard A. 2 Taylor, Laurence Robert 1 Agol, Ian 1 Bordewich, Magnus 1 Bryson, Steve 1 Casal, Arancha 1 Casson, Andrew J. 1 Curtis, Cynthia L. 1 Das Sarma, Sankar 1 Fidkowski, Lukasz M. 1 Freedman, Benedict 1 Gabai, David 1 Gamper, Lukas 1 Gils, Charlotte 1 Gompf, Robert E. 1 Guth, Lawrence David 1 Hastings, Matthew B. 1 Headrick, Matthew 1 Howards, Hugh Nelson 1 Hsiang, Wu-Chung 1 Isakov, Sergei V. 1 Kirby, Robion C. 1 Levaillant, Claire 1 Lin, Xiao-Song 1 Lurie, Jacob 1 McMullen, Curtis Tracy 1 Meeks, William Hamilton III 1 Minton, Greg 1 Morrison, Scott 1 Murphy, Emmy 1 Press, William H. 1 Sattath, Or 1 Schrijver, Alexander 1 Shtengel, Kirill 1 Simon, Steven H. 1 Slingerland, Johannes K. 1 Stern, Ady 1 Trebst, Simon 1 Troyer, Matthias 1 Welsh, Dominic J. A. 1 Wu, Yingqing 1 Yau, Shing-Tung
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#### Journals
9 Inventiones Mathematicae 9 Topology 7 Communications in Mathematical Physics 5 Mathematical Research Letters 4 Journal of Differential Geometry 4 Pacific Journal of Mathematics 4 Annals of Mathematics. Second Series 3 Topology and its Applications 3 Annals of Physics 3 Geometry & Topology 3 Foundations of Computational Mathematics 2 Commentarii Mathematici Helvetici 2 Journal of the American Mathematical Society 2 Proceedings of the National Academy of Sciences of the United States of America 2 Bulletin of the American Mathematical Society. New Series 2 Quantum Topology 1 Journal of Fluid Mechanics 1 Journal of Mathematical Physics 1 Reviews of Modern Physics 1 Bulletin of the London Mathematical Society 1 IEEE Transactions on Automatic Control 1 Memoirs of the American Mathematical Society 1 Proceedings of the American Mathematical Society 1 Discrete & Computational Geometry 1 Forum Mathematicum 1 Geometric and Functional Analysis. GAFA 1 Linear Algebra and its Applications 1 Notices of the American Mathematical Society 1 Journal of Knot Theory and its Ramifications 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Combinatorics, Probability and Computing 1 Documenta Mathematica 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Physical Review Letters 1 Algebraic & Geometric Topology 1 Bulletin of the American Mathematical Society 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 University Lecture Series 1 Journal of Topology 1 Journal of Topology and Analysis 1 Forum of Mathematics, Sigma
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#### Fields
76 Manifolds and cell complexes (57-XX) 25 Quantum Theory (81-XX) 14 Differential geometry (53-XX) 10 Computer science (68-XX) 7 Group theory and generalizations (20-XX) 7 Algebraic topology (55-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Topological groups, Lie groups (22-XX) 4 Functions of a complex variable (30-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Fluid mechanics (76-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 $K$-theory (19-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Numerical analysis (65-XX) 2 Relativity and gravitational theory (83-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory, homological algebra (18-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication, circuits (94-XX)
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You can find below the proof due to G.M; Tuynman, of the third Lie theorem.
the fact that for a simply connected Lie group $G$ not only the first de Rham cohomology space $H^1(G)={0}$ but also $H^2(G)={0}$.
http://ifile.it/hy0q139
In the Godbillon book, the Künneth theorem that identifies the cohomology of product manifolds with the tensor product of their cohomologies: $$K : H(M)\otimes H(N)\rightarrow H(M\times N)$$ If $M$ is compact, $K$ is an isomorphism. There are two things
I can not understand, among others:
1) Godbillon consider $d=K^{-1}\circ\mu^\star$, where $\mu$ is the multiplication on the Lie group $G$, and $K$ is invertible, the compactness is it essential for $K$ to be an isomorphism?!
2) Godbillon theorem shows in his page 202, with $d$, if $G$ is connected then the smallest integer $q>0$ such that $H^q(G)\neq 0$ is odd. First, $G$ must be compact? Why $H^1(G)=0$? This is not posted a consequence of the above theorem where compactness is essential!related question in math.stackexchange.com
http://math.stackexchange.com/questions/56899/elementary-proof-of-the-third-lie-theorem
1
You can find below the proof due to G.M; Tuynman, of the third Lie theorem.
The proof is similar to using the theorem of Ado, but requires an 'advanced' result:
the fact that for a simply connected Lie group $G$ not only the first de Rham cohomology space $H^1(G)={0}$ but also $H^2(G)={0}$.
http://ifile.it/hy0q139
In the Godbillon book, the Künneth theorem that identifies the cohomology of product manifolds with the tensor product of their cohomologies: $$K : H(M)\otimes H(N)\rightarrow H(M\times N)$$ If $M$ is compact, $K$ is an isomorphism. There are two things I can not understand, among others:
1) Godbillon consider $d=K^{-1}\circ\mu^\star$, where $\mu$ is the multiplication on the Lie group $G$, and $K$ is invertible, the compactness is it essential for $K$ to be an isomorphism?!
2) Godbillon theorem shows in his page 202, with $d$, if $G$ is connected then the smallest integer $q>0$ such that $H^q(G)\neq 0$ is odd. First, $G$ must be compact? Why $H^1(G)=0$? This is not a consequence of the above theorem where compactness is essential!
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# Latent variable graphical model selection via convex optimization
(2 Nov 2012), doi:10.1214/11-aos949 Key: citeulike:7866036
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### Abstract
Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of latent components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in which the latent and observed variables are jointly Gaussian, with the conditional statistics of the observed variables conditioned on the latent variables being specified by a graphical model. As a first step we give natural conditions under which such latent-variable Gaussian graphical models are identifiable given marginal statistics of only the observed variables. Essentially these conditions require that the conditional graphical model among the observed variables is sparse, while the effect of the latent variables is "spread out" over most of the observed variables. Next we propose a tractable convex program based on regularized maximum-likelihood for model selection in this latent-variable setting; the regularizer uses both the $\ell_1$ norm and the nuclear norm. Our modeling framework can be viewed as a combination of dimensionality reduction (to identify latent variables) and graphical modeling (to capture remaining statistical structure not attributable to the latent variables), and it consistently estimates both the number of latent components and the conditional graphical model structure among the observed variables. These results are applicable in the high-dimensional setting in which the number of latent/observed variables grows with the number of samples of the observed variables. The geometric properties of the algebraic varieties of sparse matrices and of low-rank matrices play an important role in our analysis.
### Citations (CiTO)
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1. Suppose a small light source is placed at the center of two transparent spheres. One sphere has a radius R, and the other a radius 2R. Energy in the form of light leaves the source at a rate P. That same power P passes through the surface of the inner sphere and reaches the outer sphere. Intensity is the power per unit area. What is the intensity at each sphere? Solve this problem by considering the following:
� How does the power passing through the inner sphere compare to the power reaching the outer sphere?
� How do the surface areas of the two spheres compare?
� In general, then, how will the intensity vary with distance from the source?
2. Since most light bulbs that you use are not true point sources of light, how do you think the answer to Question 1 would change if a typical light bulb were used?
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# Seminar
We typically have seminars on Wednesday at noon in Malone 228. All seminar announcements will be sent to the theory mailing list.
Feb
2
Tue
[Theory Seminar] Xin Li
Feb 2 @ 12:00 pm – Feb 24 @ 1:00 pm
Details TBA
Feb
17
Wed
[Theory Seminar] Aravind Srinivasan
Feb 17 @ 12:00 pm – 1:00 pm
Speaker: Aravind Srinivasan
Affiliation: University of Maryland
Title: Properties and Generalizations of the Moser-Tardos Process
Abstract: Moser and Tardos have developed an elegant and powerful algorithmic version of the Lovasz Local Lemma. Since the publication of this work, it has become apparent that this algorithm has some very interesting properties and extensions, and can be viewed as a stochastic process of independent interest. I will survey some of these, especially the ideas of “partial resampling” and the “LLL-distribution” (the properties of the output distribution of Moser-Tardos). I will draw from joint works with Haeupler and Saha, with Harris, and with Chen and Harris.
Feb
24
Wed
[Theory Seminar] Merav Parter
Feb 24 @ 12:00 pm – 1:00 pm
Title: Fault Resilient Graph Structures
Speaker: Merav Parter (MIT)
Abstract:
A fault-tolerant (FT) structure for a network is required to continue functioning following the failure of some of the network’s edges or vertices. Fault-resilience can be introduced into the network in several different ways. This talk will focus on a notion of fault-tolerance whereby the structure at hand is augmented (by adding to it various components) so that subsequent to the failure of some of the network’s vertices or edges, the surviving part of the structure is still operational. As this augmentation carries certain costs, it is desirable to minimize the number of added components.We will revise several constructions of sparse fault tolerant structures such as FT spanner and FT shortest-path trees. I will also present a new model for fault resilient network structures that mix two orthogonal protection mechanisms: (a) backup, namely, augmenting the structure with many (redundant) low-cost and fault-prone components, and (b) reinforcement, namely, acquiring high-cost but fault-resistant components. A trade-off between these two mechanisms will be presented in a concrete setting of shortest-path trees.
Mar
2
Wed
[Theory Seminar] Abhishek Jain
Mar 2 @ 12:00 pm – 1:00 pm
Details TBA
Mar
9
Wed
[Theory Seminar] Joshua Brody
Mar 9 @ 12:00 pm – 1:00 pm
Talk Title:
Dependent Random Graphs and Multiparty Pointer Jumpin
Abstract:
We initiate a study of a relaxed version of the standard Erdos-Renyi random graph model, where each edge may depend on a few other edges. We call such graphs *dependent random graphs* and give tight bounds on the clique and chromatic numbers of such graphs. Surprisingly, some of the bounds in the standard random graph model continue to hold in this relaxed setting. For example, the size of the largest clique in a dependent random graph remains roughly log(n)/log(1/p).
As an application, we give a new upper bound on communication complexity of the Multiparty Pointer Jumping (MPJ) problem in the number-on-the-forehead (NOF) model. NOF communication lies at the current frontier of our understanding of communication complexity, and MPJ is one of the canonical problems in this setting. Furthermore, sufficiently strong bounds for MPJ would have important consequences for circuit complexity.
No prior knowledge is assumed aside from basic discrete probability. I hope to motivate both random graphs and the application and demonstrate why NOF communication is an important active research area.
This talk is based on research that is joint work with Mario Sanchez.
Bio:
Joshua Brody received a bachelor’s degree in Mathematics/Computer Science from Carnegie Mellon University, a Master’s Degree in Computer Science from New York University, and a PhD in Computer Science from Dartmouth College. Prior to graduate school, he served in the Peace Corps teaching high school mathematics in Burkina Faso, West Africa. Dr. Brody is currently an Assistant Professor in the Computer Science department at Swarthmore College. His primary research area is communication complexity. Additional research interests include several areas of theoretical computer science, including streaming algorithms, property testing, and data structures.
Apr
13
Wed
[Theory Seminar] Valerio Pastro
Apr 13 @ 12:00 pm – 1:00 pm
Speaker: Valerio Pastro (Columbia University)Title: Essentially Optimal Robust Secret Sharing with Maximal Corruptions
Abstract:
In a t-out-of-n robust secret sharing scheme, a secret message is shared among n parties who can reconstruct the message by combining their shares. An adversary can adaptively corrupt up to t of the parties, get their shares, and modify them arbitrarily. The scheme should satisfy privacy, meaning that the adversary cannot learn anything about the shared message, and robustness, meaning that the adversary cannot cause the reconstruction procedure to output an incorrect message. Such schemes are only possible in the case of an honest majority, and here we focus on unconditional security in the maximal corruption setting where n=2t+1.In this scenario, to share an m-bit message with a reconstruction failure probability of at most 2−k, a known lower-bound shows that the share size must be at least m+k bits. On the other hand, all prior constructions have share size that scales linearly with the number of parties n, and the prior state-of-the-art scheme due to Cevallos et al. (EUROCRYPT ’12) achieves m+O˜(k+n).
In this work, we construct the first robust secret sharing scheme in the maximal corruption setting with n=2t+1, that avoids the linear dependence between share size and the number of parties n. In particular, we get a share size of only m+O˜(k) bits. Our scheme is computationally efficient and relies on approximation algorithms for the minimum graph bisection problem.
This talk is based on a Eurocrypt’2016 paper with authors: Allison Bishop and Valerio Pastro and Rajmohan Rajaraman and Daniel Wichs.
(This work uses some cool tools from graph theory and I encourage you all to attend. )
Apr
20
Wed
[Theory Seminar] Noga Ron-Zewi
Apr 20 @ 12:00 pm – 1:00 pm
Details TBA
Sep
14
Wed
[Theory Seminar] Samir Khuller
Sep 14 @ 12:00 pm – 1:00 pm
Speaker: Samir Khuller
Affiliation: University of Maryland College Park
Title: To do or not to do: scheduling to minimize energy
Abstract:
Traditional scheduling algorithms, especially those involving job scheduling
on parallel machines, make the assumption that the machines are always
available and try to schedule jobs to minimize specific job related metrics.
Since modern data centers consume massive amounts of energy, we consider job
scheduling problems that take energy consumption into account, turning
machines off, especially during periods of low demand. The ensuing problems
relate very closely to classical covering problems such as capacitated set
cover, and we discuss several recent results in this regard.
(This is talk covers two papers, and is joint work with Jessica Chang, Hal Gabow
and Koyel Mukherjee.)
Oct
12
Wed
[Theory Seminar] Justin Hsu
Oct 12 @ 12:00 pm – 1:00 pm
Speaker: Justin Hsu
Affiliation: University of Pennsylvania
Title: Approximate Probabilistic Coupling and Differential Privacy
Abstract: Approximate lifting is a formal verification concept for proving
differential privacy. Recently, we have explored an interesting connection:
approximate liftings are an approximate version of probabilistic coupling. As a
consequence, we can give new, “coupling” proofs of differential privacy,
simplifying and generalizing existing proofs. In this talk we will present
approximate couplings and describe how to they can be used to prove differential
privacy for the Sparse Vector mechanism, an algorithm whose existing privacy
proof is notoriously subtle.
Joint with Gilles Barthe, Marco Gaboradi, Benjamin Gregoire, and Pierre-Yves Strub.
Oct
19
Wed
[Theory Seminar] David Harris
Oct 19 @ 12:00 pm – 1:00 pm
Speaker: David Harris
Affiliation: University of Maryland College Park
Title: Improved parallel algorithms for hypergraph maximal independent set
Abstract:
Finding a maximal independent set in hypergraphs has been a long-standing algorithmic challenge. The best parallel algorithm for hypergraphs of rank $r$ was developed by Beame
and Luby (1990) and Kelsen (1992), running in time roughly $(\log n)^{r!}$. This is in RNC for fixed $r$, but is still quite expensive. We improve on the analysis of Kelsen to
show that (a slight variant) of this algorithm runs in time $(\log n)^{2^r}$. We derandomize this algorithm to achieve a deterministic algorithm running in time $(\log n)^{2^{r+3}}$ using $m^{O(1)}$ processors.
Our analysis can also apply when $r$ is slowly growing; using this in conjunction with a strategy of Bercea et al. (2015) gives a deterministic algorithm running in time
$\exp(O(\log m/\log \log m))$. This is faster than the algorithm of Bercea et al, and in addition it is deterministic. In particular, this is sub-polynomial time for graphs with
$m \leq n^{o(\log \log n)}$ edges.
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Section 2: Discrete Distributions
Printer-friendly version
In the previous section, we learned some basic probability rules, as well as some counting techniques that can be useful in determining the probability of an event using the classical approach. In this section, we'll explore discrete random variables and discrete probability distributions. The basic idea is that when certain conditions are met, we can derive formulas for calculating the probability of an event. Then, instead of returning to the basic probability rules we learned in the previous section to calculate the probability of an event, we can use the new formulas we derived, providing the certain conditions are met.
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Bandwidth of the system
1. Dec 11, 2006
LM741
hey all.
i read that the definition of the bandwidth of a system is the frequency range up until the signal's power (at DC) drops by -3dB.
This obviously only applies to a first order system , right?
Surely for a second order - it is defined as the range of frequency up until the power drops by -6dB?
thanks
2. Dec 11, 2006
Staff: Mentor
Your first statement applies to a low-pass function. If the transfer function is a bandpass, then the bandwidth is generally measured to the 3dB points on either side of the passband. It doesn't matter what order the system is, you usually use the -3dB points as the shoulders.
3. Dec 11, 2006
Staff: Mentor
4. Dec 11, 2006
LM741
Thanks - but the reason why asked the above is because i am given the following system: H(s) = 1/ (s+4)^2, and asked to find the bandwidth of the system.
It can't be w=4 (If we wish to conform to the definition of bandwidth), because at this point we have a -6dB power drop.
On the other hand, if i was given the system as: H(s) = 1/(s+4), then the bandwidth would be equal to 4, i.e w=4
thanks again
5. Dec 11, 2006
Staff: Mentor
Is your H(s) a power or voltage transfer function? Remember that -3dB is not the 1/2 signal point, it's a 1/2 power point. The signal at -3dB is $$\frac{1}{\sqrt2}$$
6. Dec 11, 2006
LM741
power = signal drops by half DC value (or DC power??).
voltage or current = signal drops to 70 percent of DC value.
They are still both regarded as -3dB points by applying the corresponding equation:
for power : 10 log(P/2)
for voltage or current :20 log(V/srt(2)).
thanks
It can be seen as a voltage ...but i don't think in this case it will make a difference...
7. Dec 12, 2006
LM741
any sugestions guys...?
8. Dec 13, 2006
Corneo
I would solve for the value of $s_0$ such that $H(s_0) = \frac {1}{\sqrt 2} H_{max}$. Since the max is clearly 1, just solve for the denominator of H(s) $$(s+4)^2 = \sqrt {2}$$
9. Dec 15, 2006
LM741
thanks - also thought about doing it that way and sticking to the definition.
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Last edited by Meztimuro
Saturday, April 18, 2020 | History
3 edition of Weak inelastic production and leptonic decays of heavy leptons found in the catalog.
Weak inelastic production and leptonic decays of heavy leptons
Amarjit Soni
# Weak inelastic production and leptonic decays of heavy leptons
Written in English
Subjects:
• Heavy leptons (Nuclear physics) -- Decay.,
• Inelastic cross sections.
• Edition Notes
Classifications The Physical Object Statement Amarjit Soni. LC Classifications QC793.5.L425 S65 Pagination 85, 11 leaves, [3] leaves of plates : Number of Pages 85 Open Library OL4296650M LC Control Number 78324855
This experiment studied the quark structure of the p meson, using the Drell-Yan process of m + m-pair creation via a virtual photon in p-nucleus collisions. The data from E demonstrated that the momentum distribution of the valence quarks inside the pion extends to much larger fraction x of the pion's total momentum than is the case for quarks inside a proton or neutron. ISBN: OCLC Number: Notes: Papers presented at the International Symposium on Weak and Electromagnetic Interactions in Nuclei held in Heidelberg, July ; sponsored by International Union of Pure and Applied Physics and European Physical Society. Non-leptonic B-decays at two loops in QCD: Theory seminar, Z"urich University: Tobias Huber: Towards precision phenomenology in non-leptonic and rare B decays: EW and Flavor Physics at CEPC, Beijing, China: Tobias Huber: Non-leptonic B-decays at two loops in QCD: Theory seminar, Durham University: Tobias Huber. Preon models have been around since at least which is the date of publication of a paper by Pati and Salam that proposed a substructure to quarks and leptons. A book on preon theories was published in by D'Souza and Kalman, and I would refer you to that book as a good place to read about preon history.
Measurement of the Michel parameters in leptonic tau decays. Search for unstable heavy and excited leptons in e+e- collisions at √s = GeV. European Physical Journal C. Tests of the standard B* production in Z0 decays.
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### Weak inelastic production and leptonic decays of heavy leptons by Amarjit Soni Download PDF EPUB FB2
The W and Z bosons are together known as the weak or more generally as the intermediate vector elementary particles mediate the weak interaction; the respective symbols are W + W −, and Z 0The W ± bosons have either a positive or negative electric charge of 1 elementary charge and are each other's Z 0 boson is electrically neutral and Composition: Elementary particle.
Publisher Summary. Most leptonic decays of strange particles are strangeness changing. The interaction that gives rise to these decays is the coupling of us current to the leptonic currents e⩗ and μ⩗.All strangeness-changing leptonic decays occur through the us current, which changes strangeness by unity.
The chapter discusses that there are certain selection rules to which the. Inclusive weak decays of heavy hadrons with power suppressed terms at NLO Article (PDF Available) in Physical Review D 92(5).
Abstract. Quarks and leptons are equally affected by the weak interaction. At the beginning of this chapter we first present the properties of the three charged leptons and the associated neutrinos followed by a discussion of the various types of weak interactions: leptonic, semileptonic and non-leptonic : Bogdan Povh, Klaus Rith, Christoph Scholz, Frank Zetsche, Martin Lavelle.
Leptonic and semileptonic decays of B mesons. This scheme hints us to review all the weak decays involved the unnatural heavy-light mesons. In this second edition, many chapters (e.g. on electroweak unification) have been revised to bring them up to date.
In particular, the chapters on neutrino physics, particle mixing and CP violation, and weak decays of heavy flavors have been rewritten incorporating new material and new data. The heavy quark effective theory has been included. When the initial and final hadrons of a semi-leptonic decay belong to the same isotopic multiplet (such as the neutron and proton in the β-decay n → pe − ν), we can introduce the concept of the weak charge.
The weak charge is defined as the time-like component of the 4-vector V α for q = 0. The weak charge determines the strength of the. The book deals with this progress but includes chapters which provide the necessary background material to modern particle physics.
Particle physics forms an essential part of physics curriculum. This is a textbook but will also be useful for people working in this field and for nuclear physicists, particularly those who work on topics.
Abstract. This paper discusses the work done in high energy physics at the University of Oregon over the post year.
Some of the topics briefly discussed are: string phenomenology, horizontal symmetry, heavy quark decays, neutrino counting and new quarks and leptons, treatment of heavy particles and w-bosons as constituents of hadrons, higher twist corrections to heavy. The J/ψ (J/psi) meson / ˈ dʒ eɪ ˈ s aɪ ˈ m iː z ɒ n / or psion is a subatomic particle, a flavor-neutral meson consisting of a charm quark and a charm formed by a bound state of a charm quark and a charm anti-quark are generally known as "charmonium".The J/ψ is the most common form of charmonium, due to its spin of 1 and its low rest J/ψDiscovered: SLAC: Burton Richter et al.
Lepton pair production Jets in pp collisions Current and constituent quarks Problems 8 9 Weak interactions: quarks and leptons Charged current reactions W±–lepton interactions Lepton–quark symmetry and mixing W boson decays Selection rules in weak.
Describing the fundamental theory of particle physics and its applications, this book provides a detailed account of the Standard Model, focusing on techniques that can produce information about real observed by: The Standard Model: A Primer The standard model provides the modern understanding of all of the inter-actions of subatomic particles, except those due to gravity.
The theory has emerged as the best distillation of decades of research. This book uses the standard model as a vehicle for introducing quantum field theory. The temporal-spectral evolution of the prompt emission of gamma-ray bursts is simulated numerically for both leptonic and hadronic models.
For weak enough magnetic fields, leptonic models can reproduce the few seconds delay of the onset of GeV photon emission observed by Fermi-LAT, due to the slow growth of the target photon field for inverse Compton scattering. B (); In *IthacaProceedings, Lepton and Photon Interactions At High Energies*,; IN *BOLOGNAPROCEEDINGS, FIFTY YEARS OF WEAK-INTERACTION PHYSICS* The Table of Contents for the book is as follows: * VOLUME I * Foreword * Conference Organization * Welcome Address * PLENARY SESSIONS * Pl New Results in Spectroscopy * New Results in Spectroscopy * Pl Soft Interactions and Diffraction Phenomena * Soft Interactions and Diffraction Phenomena * Pl Spin Structure of the Nucleon * Spin.
The muon μ − and its antiparticle 1 the μ + both have a mass of only 7 MeV∕c 2 and they are produced in all usual $$\mathrm{e}^{+}\mathrm{e}^{-}$$ storage ring experiments.
They penetrate matter very easily, 2 whereas electrons because of their small mass and hadrons because of the strong interaction have much smaller ranges.
After that of the neutron, theirs is the longest Author: Bogdan Povh, Klaus Rith, Christoph Scholz, Frank Zetsche, Martin Lavelle.
A spin-0 Higgs boson decays into two spin-1 W bosons with antiparallel polarizations. The positive leptons are preferably emitted into the forward hemisphere with respect to the W spin while the negative leptons tend to fly backwards. Thus the two leptons prefer to fly into the same hemisphere, close to one another.
Neutrino Physics I. Gil-Botella Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, Madrid, Spain Abstract The fundamental properties of neutrinos are reviewed in these lectures.
The first part is focused on the basic characteristics of neutrinos in the Standard Model and how neutrinos are detected. The weak currents; 3. The quark model; Part II.
Field Theories with Global or Local Symmetries: 4. Yang-Mills theories; 5. Spontaneous breaking of symmetries; 6. Construction of the model; 7. The Higgs mechanism in the Glashow-Salam-Weinberg model; 8.
The Leptonic sector; 9. Incorporating hadrons; Part III. Experimental Consequences and. The fundamental leptonic charged weak vertex is W‘, i.e. a Wboson can decay into a lepton and its corresponding antineutrino. This vertex mediates the decay of the muon.
Finally, the quark charged weak vertex converts an up-type quark to a down-type quark, e.g. Wud0. However, the quarks are de ned in the mass basis, while this interaction is. Muons and neutrinos from cosmic ray interactions in the atmosphere originate from decays of mesons in air-showers.
Sibyllc aims to give a precise description of hadronic interactions in the relevant phase space for conventional and prompt leptons in light of new accelerator data, including that from the LHC.
Sibyll is designed primarily as an event generator for use in Author: Groundai. Leptonic decays of pseudoscalar mesons also enable powerful tests of LU.
The most stringent constraints derive from the study of leptonic decays of charged pions or kaons, which are helicity suppressed in the SM. The ratio of the partial decay widths of and, for which hadronic uncertainties cancel, can be precisely computed in the SM.
Summary of Working Group 5: Heavy Flavours of fb 1 a relative precision of 1 to 5% on jV cbjis possible, where the variation arises from assumptions about the performance of the charm-tagging algorithm [34].
b and c decays Our final topic is the study of weak decays of b and c quarks, otherwise known as flavour : V. Bhardwaj, J. Libby, J. Virto. Book Description. An Introduction to the Standard Model of Particle Physics familiarizes readers with what is considered tested and accepted and in so doing, gives them a grounding in particle physics in general.
Whenever possible, Dr. Mann takes an historical approach showing how the model is linked to the physics that most of us have learned in less challenging areas. Lepton pair production Jets in pp collisions Current and constituent quarks Problems 8 9 Weak interactions: quarks and leptons Charged current reactions W±–lepton interactions Lepton–quark symmetry and mixing W boson decays Selection rules in weak Brand: Wiley.
Extremely weak and super-efficient production of keV sterile neutrino: phase transition and induced parametric resonance creation. Higgs boson production in decays to two tau leptons using the ATLAS detector (in session "Higgs Physics") Lattice calculation of form factors for semi-leptonic decays B \to D^(\ast) using improved heavy.
23) Some New Isospin Bounds on Multipion Production (with A. Pais), Physical Review D6 (). 24) Spontaneously Broken Gauge Theories of Weak Interactions and Heavy Leptons (with J.D.
Bjorken), Physical Review D7 (). 25) Deep Inelastic Scattering, the Subtraction of Divergent Sum Rules and Chiral Symmetry Breaking in. Featuring a wide-ranging treatment of electroweak symmetry breaking, the physics of the Higgs boson, and the importance of the 1-TeV scale, the book moves beyond established knowledge and investigates the path toward unified theories of.
The Internet Archive offers o, freely downloadable books and texts. There is also a collection of million modern eBooks that may be borrowed by anyone with a free account. Borrow a Book Books on Internet Archive are offered in. An Introduction to the Standard Model of Particle Physics familiarizes readers with what is considered tested and accepted and in so doing, gives them a grounding in particle physics in general.
Whenever possible, Dr. Mann takes an historical approach showing how the model is linked to the physics that most of us have learned in less challenging areas. Mann reviews. 40th International Conference on High Energy Physics ICHEP is a series of international conferences organized by the C11 commission of the International Union of Pure and Applied Physics (IUPAP).
It has been held every two years since more than 50 years, and is the reference conference of particle physics where most relevant results are presented. At ICHEP, physicists. Full text of "Introduction To Particle Physics" See other formats.
The European Organization for Nuclear Research, known as CERN, is a European research organization that operates the largest particle physics laboratory in the ished inthe organization is based in a northwest suburb of Geneva on the Franco–Swiss border and has 23 member states.
Israel is the only non-European country granted full membership. Hardware Offline Software Physics Physics Book. Research Status Run Operation Data Sets Talks Publications Account Meetings Hypernews Documentation Other Links.
4 (6 ratings by Charged Leptonic Weak Interactions Neutrino-Electron Scattering Muon Decay Appendix: Mathematical Tools for Weak Interactions Appendix: 3-body phase space decay Questions Charged Weak Interactions of Quarks and Leptons Neutron Decay Pion Decay Quark and 4/5(6).
You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
Book description Fully updated for the second edition, this book introduces the growing and dynamic field of particle astrophysics. It provides an overview of high-energy nuclei, photons and neutrinos, including their origins, their propagation in the cosmos, their detection on Earth and their relation to each by: Since the tauonic lepton number is conserved in weak decays, a tau neutrino is always created when a tau decays.
The branching ratio of the common purely leptonic tau decays are: % for decay into a tau neutrino, electron and electron antineutrino; % for decay into a tau neutrino, muon and muon antineutrino.
Erratum to: Search for heavy resonances decaying into a W or Z boson and a Higgs boson in final states with leptons and b-jets in 36 fb −1 of √s = 13 TeV pp collisions with the ATLAS detector (Journal of High Energy Physics, (),3, (), /JHEP03()).
nameOfConference. 24) Spontaneously Broken Gauge Theories of Weak Interactions and Heavy Leptons (with J.D. Bjorken), Physical Review. D7. (). 25) Deep Inelastic Scattering, the Subtraction of Divergent Sum Rules and Chiral Symmetry Breaking in the Gluon Model (with R.L.
Jaffe), Physical Review. D7. ().Heavy-Flavor Pair Production. The phrase heavy-flavor conventionally refers to events involving the three heaviest quarks, that is the charm, bottom and the so far unobserved top quark.
Events are mediated by the exchange of photons or bosons which fuse with a gluon radiated by the proton. This gives the BGF mechanism its name.2. Charm Production and fragmentation 25 4. 3. Effective field theories (EFTh) 25 4. 4. 1/NC expansions 26 4. 5. Heavy quark symmetry (HQS) 27 4.
6. Heavy quark expansions (HQE) 27 4. QCD for heavy quarks 28 4. The Operator Product Expansion (OPE) and weak decays of heavy flavour hadrons 29 4.
Heavy Quark Parameters (HQP.
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# What is the simplest analog circuit for integer addition modular 2?
This probably is a rudimentary question. I would like to have a simple analog (switch) circuit for addition modular 2, or $a_1+a_2+\cdots +a_n$ (mod 2). Certainly, digital transistors can accomplish this, but I would prefer analog devices if the circuit is simpler. In practical terms, I would like to design a switch circuit to control a light, where fixing all other switches, any one of them can switch the light on and off. For $n=2$ or 2 switches, someone earlier has already suggested using two back to back single-pole-double-throw switches.
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May not be the simplest, but implementing n input xor gate using transistors is a solution. – nidhin Jul 12 '14 at 14:52
@nidhin, yes, but I would prefer simpler analog circuit. – Hans Jul 12 '14 at 15:34
For 4 places see below: -
simulate this circuit – Schematic created using CircuitLab
For 3 places remove one of the two pole switches. For more than 4 just keep repeating the 2 pole switches.
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Dang it. I just spent an hour noodling on this and just came up with this. Congrats for beating me to it. At least I have the satisfaction of solving this interesting house wiring issue. Btw, was this a well known design you've known for years or did you just come up with this? +1 – horta Jul 12 '14 at 16:56
@horta - well done for figuring it out dude but on this occasion knowledge has beaten intelligence LOL – Andy aka Jul 12 '14 at 17:36
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# Math Help - Equation of two lines tangent to a circle
1. ## Equation of two lines tangent to a circle
The question:
There are two tangent lines from the point (0,1) to the circle x^2 + (y+1)^2=1 [centered at (0,-1) with a radius of one]. Find equations of these lines by using the fact that each tangent line intersects the circle in exactly one point.
There is also a graph but it shows pretty much what the question says. I have no idea how I can find the slopes of these tangent lines
2. If we solve the circle equation for y, we get $y=\sqrt{1-x^{2}}-1$
We can use $y-y_{1}=m(x-x_{1})$, plug in all of our info wrt x and solve for x.
Where m is the derivative of y, $y_{1}=1, \;\ x_{1}=0$
$\underbrace{\sqrt{1-x^{2}}-1}_{\text{y}}-1=\frac{-x}{\sqrt{1-x^{2}}}(x-0)$
Now, solve for x. There will be the two values of x.
This will be the two x values where the lines are tangent to the circle.
Then, you will have all the info needed to find the line equations.
3. Ah thank you very much!
But I'm wondering if there is a way to find the derivative without using calculus since this problem was in the review section of the calc book?
4. Originally Posted by atruenut
Ah thank you very much!
But I'm wondering if there is a way to find the derivative without using calculus since this problem was in the review section of the calc book?
From the equation of the circle you know that the center of the circle is: C(0, -1).
Let T(x, y) denote the tangent point on the circle then the slope of $\overline{TC}$ is:
$m_{TC}=\dfrac{y-x_C}{x-x_C}=\dfrac{y-(-1)}{x-0}$
Since T is placed on the circle line the coordinates of T are $T(x, \sqrt{1-x^2} - 1)$
Therefore
$m_{TC}=\dfrac{\sqrt{1-x^2} - 1-(-1)}{x}=\dfrac{\sqrt{1-x^2}} x$
The line TC is perpendicular to the tangent because TC = r. Therefore the slope of the tangent must be the negative reciprocal of the slope of TC:
$m_t=-\dfrac x{\sqrt{1-x^2}}$
5. ## Analytic approach
Originally Posted by atruenut
The question:
There are two tangent lines from the point (0,1) to the circle x^2 + (y+1)^2=1 [centered at (0,-1) with a radius of one]. Find equations of these lines by using the fact that each tangent line intersects the circle in exactly one point.
There is also a graph but it shows pretty much what the question says. I have no idea how I can find the slopes of these tangent lines
Let $C:~x^{2}+(y+1)^{2}=1$.
Clearly, the center of the circle is $M=(0,-1)$ and the radius is $r=1$.
Let $Q:=(q_{1},q_{2})$ be an arbitrary point on $C$.
Then, it is easy to see that the tangent line of the circle at $Q$ is given by
$\langle\underset{\overrightarrow{QX}}{\underbrace{ (x-q_{1},y-q_{2})}},\underset{\overrightarrow{MQ}}{\underbrac e{(q_{1},q_{2}+1)}}\rangle=0$
or simply
$q_{1}(x-q_{1})+(y-q_{2})(q_{2}+1)=0$.......................(*)
We want this line pass through the point $(0,1)$.
Then, we have $0=q_{1}^{2}+(q_{2}-1)(q_{2}+1)=q_{1}^{2}+q_{2}^{2}-1$, using the fact that $Q\in C$, we have $q_{1}^{2}+q_{2}^{2}=-2q_{2}$, therefore, we obtain $q_{2}=-1/2$.
Using this in the circle's equation, we have $q_{1}=\pm\sqrt{3}/2$.
Using $Q=(-1/2,\pm\sqrt{3}/2)$ in (*), we get the desired tangent line equations.
6. Hello, atruenut!
There are two tangent lines from the point (0,1) to the circle $x^2 + (y+1)^2\:=\:1$
Find equations of these tangents.
Code:
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P * (0,1)
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. / | \
/ | \
/ | \
/ | \
- - - - / - * * * - \ - - - - - -
/* | *\
o | o A
* * | * *
* | *
* * | * *
* C *(0,-1) *
* | *
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* | *
* | *
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* * *
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The center of the circle is: $C(0,-1)$
Its radius is: $CA = 1$
A radius is perpendicular to a tangent at the point of tangency.
. . Hence: . $\angle CAP \:=\:90^o$
In right triangle $CAP$ we have: . $CA = 1,\;CP = 2$
. . Hence, $\Delta CAP$ is a 30-60 right triangle . . . $\angle APC = 30^o$
You should be able to determine the slope of $PA$ . . . right?
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# What is the density of a piece of wood that has a mass of 25.0 g and a volume of 29.4 cm^3?
Mar 1, 2016
0.850 g/(cm^3
#### Explanation:
The problem can be solved using the formula;
$D e n s i t y = \frac{m a s s}{v o l u m e}$.
Since 2 of the data are already provided in the problem, just plug in the values to the formula.
Rearrangement of the formula from its standard form is not necessary at all.
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## Installing the Indian rupee symbol on Windows
Last Sunday, I published a new puzzle at http://cotpi.com/p/54/ that uses the Indian rupee symbol ₹. It appeared fine on Iceweasel 10 as well as Google Chrome 20 on Debian testing distribution (Wheezy). However, Firefox 12 as well as Google Chrome 19 failed to render the symbol on Windows 7 Enterprise Service Pack 1.
To resolve this, I downloaded an update for my version of Windows from KB2496898, installed it and rebooted the computer. KB2496898 lists the updates for other versions of Windows as well.
## Implication of implications
Last night, I came across a simple propositional logic problem concerned with the validity of the statement:
$\bigl((A \implies B) \land (B \implies C)\bigr) \iff (A \implies C).$
At first, I thought it is valid. But on drawing the truth table, I was surprised to see that it isn't valid.
$$A$$ $$B$$ $$C$$ $$A \implies B$$ $$B \implies C$$ $$A \implies C$$ $$(A \implies B) \land (B \implies C)$$ $$\bigl((A \implies B) \land (B \implies C)\bigr)$$ $$\iff$$ $$(A \implies C)$$ T T T T T T T T T T F T F F F T T F T F T T F F T F F F T F F T F T T T T T T T F T F T F T F F F F T T T T T T F F F T T T T T
My intuition had failed. The truth table shows that there are two cases in which the statement is false.
### Case 1: $$(A \implies C) \land (B \implies C) \land \lnot(A \implies B)$$
In this case, $$A$$ implies $$C$$ and $$B$$ implies $$C$$, but $$A$$ does not imply $$B$$. This corresponds to the third row in the truth table. It makes sense. Two things can imply a third thing but they need not imply each other. For example, rain may imply wet soil and snow may imply wet soil as well, but rain need not imply snow. Here is another example that demonstrates this.
The following two statements are true for any integer $$x$$.
$4 \mid x \implies 2 \mid x. \\ 6 \mid x \implies 2 \mid x.$
But the following statement is false when $$x \equiv 4 \pmod{12}$$ or $$x \equiv 8 \pmod{12}$$.
$4 \mid x \implies 6 \mid x.$
In other words, if an integer is a multiple of $$4$$ as well as a multiple of $$6$$, then it is also a multiple of $$2$$. But this is not equivalent to claiming that if an integer is a multiple of $$4$$, then it is also a multiple of $$6$$. Such a claim is not correct as we can confirm for $$x \in \{4, 8, 16, 20, 28, 32, \dots\}$$.
### Case 2: $$(A \implies B) \land (A \implies C) \land \lnot(B \implies C)$$
In this case, $$A$$ implies $$B$$ as well as $$C$$ but $$B$$ does not imply $$C$$. This corresponds to the sixth row in the truth table. It makes sense as well. One thing can imply two other things but those two things need not imply each other. For example, rain may imply wet soil and flooded rivers but wet soil need not imply flooded rivers. The soil could be wet due to irrigation sprinklers. Once again, here is a mathematical example to demonstrate this.
The following two statements are true for any integer x.
$6 \mid x \implies 2 \mid x. \\ 6 \mid x \implies 3 \mid x.$
But the following statement is false when $$x$$ is an odd multiple of $$3$$.
$2 \mid x \implies 3 \mid x.$
In other words, if an integer is a multiple of 6, then it is a multiple of 2 as well as 3. But this is not equivalent to claiming that if an integer is a multiple of 2, then it is also a multiple of 3. Such a claim is clearly false as we can confirm for $$x \in \{3, 9, 15, 21, \dots\}$$.
### Encoding intuition correctly
My intuition incorrectly concluded that the $$\bigl((A \implies B) \land (B \implies C)\bigr) \iff (A \implies C)$$ is valid because I was not translating the given statement correctly in my mind. I was thinking that if $$A$$ implies $$B$$ and $$B$$ implies $$C$$, of course $$A$$ must also imply $$C$$. This is true but this is not what the given statement represents. The given statement means something more than this. In addition to what I thought, it also means that if $$A$$ does not imply $$B$$ or $$B$$ does not imply $$C$$, then $$A$$ does not imply $$C$$ as well. This however doesn't happen. The truth table shows that even though $$A$$ does not imply $$B$$ or $$B$$ does not imply $$C$$, it is possible that $$A$$ implies $$C$$.
As far as my intuition is concerned, the following would be the right way to represent what I was thinking.
$\bigl((A \implies B) \land (B \implies C)\bigr) \implies (A \implies C).$
Indeed, this statement is valid as can be seen from the truth table below.
$$A$$$$B$$$$C$$ $$A \implies B$$$$B \implies C$$$$A \implies C$$ $$(A \implies B) \land (B \implies C)$$ $$\bigl((A \implies B) \land (B \implies C)\bigr)$$ $$\implies$$ $$(A \implies C)$$
TTT TTT T T
TTF TFF F T
TFT FTT F T
TFF FTF F T
FTT TTT T T
FTF TFT F T
FFT TTT T T
FFF TTT T T
## Code wrap behaviour
When the HTML pre element uses the CSS width and word-wrap: break-word properties, the long lines of code wrap in Chrome and IE6 but not in Firefox.
Here is a sample page that demonstrates this: http://susam.in/files/notes/css-hacks/pre-word-wrap/pre-word-wrap.html. The CSS code for the HTML pre element is as follows.
pre {
border: 1px solid black;
background: #ebebeb;
width: 20em;
overflow: auto;
color: blue;
}
pre.wrap {
word-wrap: break-word;
}
The first box in each output below use the wrap class. The second ones in each is a plain pre element.
Output in Firefox 3.6
Output in Chrome 11
Output in Internet Explorer 6
[css]
## Long code overflow behaviour
When the HTML pre element uses the CSS width and overflow: auto properties, code that doesn't fit within the width of the pre element is clipped and a scroll-bar appears which can be used to view the remaining code.
However, when it contains only one line of code, we see a couple of issues in Firefox 3.6 and IE6. Here is a sample page that demonstrates the issue: http://susam.in/files/notes/css-hacks/pre-overflow/pre-overflow.html. Here is the CSS used for the HTML pre element.
pre {
border: 1px solid black;
background: #ddccff;
width: 20em;
overflow: auto;
}
Firefox 3.6 doesn't display the scroll-bar if the pre element contains only one line of code. It is still possible to scroll the code though by using the arrow-keys on the keyboard or selecting text in the code with the mouse and moving right.
Output in Firefox 3.6
Chrome does the right thing and displays the scroll-bar.
Output in Chrome 11
Internet Explorer 6 always hides the last line of the code behind the scroll-bar. Therefore, when there is only one line of code, the scroll-bar hides this only line of code and no code is visible.
Output in Internet Explorer 6
[css]
## Long word breaking float in IE
If there are two HTML div elements placed side-by-side using float: left and float: right, a long word in one of the div elements breaks the floating property of the other in Internet Explorer 6 as well as Internet Explorer 8.
Here is a sample page that demonstrates this issue: http://susam.in/files/notes/css-hacks/long-word-and-sidebar/long-word-and-sidebar.html. Here is the CSS used for both the HTML div elements.
#id1 {
float: left;
width: 65%;
border: 1px solid #000080;
background: #ffcc00;
padding: 2px;
}
#id2 {
float: right;
width: 30%;
border: 1px solid #008000;
background: #ccccff;
padding: 2px;
}
In each output shown below, the box on the left has its ID as id1 and the one on the right has its ID as id2. The box on the left has a long word.
Output in Firefox 3.6
The sidebar with its ID as id2 is intact in Firefox even though the long word has spilled outside the box on the left. However, the layout breaks in Internet Explorer 8 as can be seen below.
Output in Internet Explorer 8
The fix involves allowing long words to break and wrap.
#id1 {
float: left;
width: 65%;
border: 1px solid #000080;
background: #ffcc00;
padding: 2px;
word-wrap: break-word;
}
Here is a page that demonstrates the fix: http://susam.in/files/notes/css-hacks/long-word-and-sidebar/long-word-and-sidebar-fixed.html.
Output in Firefox 3.6
Output in Internet Explorer 8
[css]
Newer | Older
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## Is it considered bad practice to have a wallet "cloned" on both a smartphone and a desktop PC?
1
1
Can I use my wallet on different computers?
Can wallets be shared by different machines?
...but what I'm asking regards popular wallets as BitPay and Electrum, that have both the desktop and mobile app, permitting to export and import a wallet. Nothing that takes into account messing with any wallet.dat file.
I'm currently doing this with a BitPay wallet, and it seems it works good. When a transaction occurs (i.e. I receive funds) this is notified on both platforms (I think it's related to how those wallets works; I'm referring to the Bitcore Wallet Service).
I also read about the notorious quote "not a good idea", but I'm not sure of this refers to different type of wallets or what else...
Any clarification on this is more than welcome.
0
It is merely a question of security. If your copy of the private key in wallet A (phone) is compromised, you can lose your coins. If your copy of the private key in wallet B (PC) is compromised, you can lose your coins.
Assuming both copies are secure, you basically just have a backup of your private key.
As for whether or not having two copies like that is secure or "best practice", that depends a lot on how you handle your computers, and there are better experts out there that can answer that.
One thing you cannot do is double spend. If they use the same private key, one wallet is the same as the other, and trying to spend out of both will result in an unconfirmed transaction on one of them.
Hi, thanks. This is what I thought, so I'm happy I have an answer in regards. So you're saying that synchronization is by design, and there's nothing to worry about, right? – dentex – 2017-07-29T07:54:08.533
@dentex, the protection against double spending is certainly by design... the ability to backup a private key and the fact that the private key is the single thing that allows you to "unlock" a coin and spend it is just a mathematical fact... made use of in the design. You can have as many copies of the private key as you want, just don't let anyone else have access to it, including an app you may not trust. – Smack Jack – 2017-07-29T08:20:18.570
Stack Exchange has turned into garbage – Smack Jack – 2017-07-31T01:02:24.700
OMG. What happened? I hope it's nothing related to this Q. – dentex – 2017-07-31T04:48:29.170
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# Lax pair and compatibility for KdV
#### dwsmith
##### Well-known member
\begin{align}
u_t + u_{xxx} + 6uu_x &= 0\\
L &= \partial_{xx} + u_t\\
M &= -4\partial_{xxx} - 3(2u\partial_x + u_x)
\end{align}
For the $$L$$ operator, should that be $$u$$ not $$u_t$$?
\begin{align}
\partial_{xx}\psi &= (\lambda - u)\psi\\
\partial_t\psi &= (-4\partial_{xxx} - 6u\partial_x - 3u_x)\psi
\end{align}
Also, where did $$\lambda$$ come from?
#### Ackbach
##### Indicium Physicus
Staff member
Yes, typically $L$ is chosen to be a Schrödinger operator; in your case, since you're using $u$ as the variable in KdV, you would usually write $L= \partial_{xx}+v$. So, just to be clear (and it's usually a good idea to write operators with the test function, since operators are such slippery characters), we have that $Lu=(\partial_{xx}+v)u=u_{xx}+uv$. I say this is typical. However, if you find a different $L$ and $M$ that, when plugged into the Lax equation, reproduce your pde, then those are fine.
The $\lambda$ comes from one of the two Lax equations: $Lv=\lambda v$. It's called the eigenvalue.
#### dwsmith
##### Well-known member
Yes, typically $L$ is chosen to be a Schrödinger operator; in your case, since you're using $u$ as the variable in KdV, you would usually write $L= \partial_{xx}+v$. So, just to be clear (and it's usually a good idea to write operators with the test function, since operators are such slippery characters), we have that $Lu=(\partial_{xx}+v)u=u_{xx}+uv$. I say this is typical. However, if you find a different $L$ and $M$ that, when plugged into the Lax equation, reproduce your pde, then those are fine.
The $\lambda$ comes from one of the two Lax equations: $Lv=\lambda v$. It's called the eigenvalue.
So are my first L and M ok then?
#### Ackbach
##### Indicium Physicus
Staff member
So are my first L and M ok then?
To find out if they work, you have a significant computation ahead of you. As a guide, in my Ph.D. dissertation, I compute whether the standard Schrödinger operator and its mate produce the KdV equation when plugged into Lax's equation. You can follow that program and see if those operators work. I'd be curious to know, so if you could please post the results, I'd be most grateful.
#### dwsmith
##### Well-known member
To find out if they work, you have a significant computation ahead of you. As a guide, in my Ph.D. dissertation, I compute whether the standard Schrödinger operator and its mate produce the KdV equation when plugged into Lax's equation. You can follow that program and see if those operators work. I'd be curious to know, so if you could please post the results, I'd be most grateful.
So I found $$LM$$, $$ML$$, and $$L_t$$ but I don't think I did something right or there is a simplification I don't see.
\begin{align}
LMv &= -4v_{xxxxx} - 6u_{xx}v_x - 12u_xv_{xx} - 6uv_{xxx} - 3u_{xxx} - 4u_tv_{xxx} - 6u_tuv_x - 3u_tu_xv\\
-MLv &= 4v_{xxxxx} + 4u_{txxx}v + 4u_tv_{xxx} + 6uu_{tx}v + 6uu_tv_x + 3u_xv_{xx} + 3u_xu_tv\\
[LM - ML]v &= 4u_{txxx}v + 6uu_{tx}v - 6u_{xx}v_x - 9u_xv_{xx} - 3u_{xxx}\\
L_tv &= v_{xxt} + u_{tt}v\\
[L_t + [L,M]]v &= v_{xxt} + u_{tt}v + 4u_{txxx}v + 6uu_{tx}v - 6u_{xx}v_x - 9u_xv_{xx} - 3u_{xxx}
\end{align}
#### Ackbach
##### Indicium Physicus
Staff member
Well, one thing right away I can see. If you look at the bottom of page 6 of my dissertation, you will see that when you compute $L_{t}$, everywhere you see just a $\partial_{x}$, it vanishes. That is, if $L=-\partial_{x}^{2}+u$, then $L_{t}=u_{t}$. It is not true that $L_{t}=-\partial_{t} \partial_{x}^{2}+u_{t}$.
Therefore, by analogy in your case, if you have $L=\partial_{x}^{2}+u_{t}$, then you should have $L_{t}=u_{tt}$.
Checking one or two other computations (you would make me do that, wouldn't you? ). You must assemble $LM$, which in your case is
$$LMv= \left( \partial_{x}^{2}+u_{t} \right) \left( -4 \partial_{x}^{3}-6u \partial_{x}-3u_{x} \right)v= \left[ -4 \partial_{x}^{5}-6\partial_{x}^{2}u \partial_{x} -3 \partial_{x}^{2}u_{x}-4u_{t} \partial_{x}^{3}-6u_{t}u \partial_{x}-3u_{t}u_{x}\right]v.$$
The second and third terms require more computation (you want the $\partial_{x}^{n}$ parts to be at the far right of the expressions). So, you must have the following:
\begin{align*}
\partial_{x}^{2}u \partial_{x}&=u_{xx}\partial_{x}+2u_{x} \partial_{x}^{2}+u \partial_{x}^{3} \quad \text{(Equation 1.1.15 in the dissertation)}\\
\partial_{x}^{2}u&=u_{xx}+2u_{x} \partial_{x}+ \partial_{x}^{2}, \quad \text{so by analogy, we have}\\
\partial_{x}^{2}u_{x}&=u_{xxx}+2u_{xx} \partial_{x}+ \partial_{x}^{2}.
\end{align*}
Dropping these into the previous $LM$ expression yields
\begin{align*}
LMv&=\left[ -4 \partial_{x}^{5}-6(u_{xx}\partial_{x}+2u_{x} \partial_{x}^{2}+u \partial_{x}^{3}) -3 (u_{xxx}+2u_{xx} \partial_{x}+ \partial_{x}^{2})-4u_{t} \partial_{x}^{3}-6u_{t}u \partial_{x}-3u_{t}u_{x}\right]v \\
&=\left[ -4 \partial_{x}^{5}-6u_{xx}\partial_{x}-12u_{x} \partial_{x}^{2}-6u \partial_{x}^{3} -3 u_{xxx}-6u_{xx} \partial_{x}-3 \partial_{x}^{2}-4u_{t} \partial_{x}^{3}-6u_{t}u \partial_{x}-3u_{t}u_{x}\right]v \\
&=\left[ -4 \partial_{x}^{5}-12u_{xx}\partial_{x}-12u_{x} \partial_{x}^{2}-6u \partial_{x}^{3} -3 u_{xxx}-3 \partial_{x}^{2}-4u_{t} \partial_{x}^{3}-6u_{t}u \partial_{x}-3u_{t}u_{x}\right]v \\
&=-4v_{xxxxx}-12u_{xx}v_{x}-12u_{x}v_{xx}-6uv_{xxx}-3u_{xxx}v-3v_{xx}-4u_{t}v_{xxx}-6u_{t}uv_{x}-3u_{t}u_{x}v.
\end{align*}
You can see there are a couple of differences between this expression and yours. Double-check your $MLv$ equation also.
#### Ackbach
##### Indicium Physicus
Staff member
For $MLv$, I get
\begin{align*}
MLv&= \left( -4 \partial_{x}^{3}-6u \partial_{x}-3u_{x} \right) \left( \partial_{x}^{2}+u_{t} \right)v \\
&= \left( -4 \partial_{x}^{5}-4 \partial_{x}^{3}u_{t}-6u \partial_{x}^{3}-6u \partial_{x} u_{t}-3u_{x} \partial_{x}^{2}-3u_{x}u_{t} \right) v.
\end{align*}
We need two of these finished out:
\begin{align*}
\partial_{x}^{3} u&=u_{xxx}+3u_{xx} \partial_{x}+3u_{x} \partial_{x}^{2}+u \partial_{x}^{3}, \quad \text{so by analogy}\\
\partial_{x}^{3} u_{t}&=u_{txxx}+3u_{txx} \partial_{x}+3u_{tx} \partial_{x}^{2}+u_{t} \partial_{x}^{3}.
\end{align*}
I don't have an analogy for $u \partial_{x} u_{t}$, so here goes:
$$(u \partial_{x} u_{t})v=u \partial_{x}(u_{t}v)=u(u_{tx}v+u_{t}v_{x})= (uu_{tx}+uu_{t} \partial_{x})v,$$
and hence
$$u \partial_{x} u_{t}=uu_{tx}+uu_{t} \partial_{x}.$$
Dropping these into $MLv$ yields
\begin{align*}
MLv&=\left( -4 \partial_{x}^{5}-4 (u_{txxx}+3u_{txx} \partial_{x}+3u_{tx} \partial_{x}^{2}+u_{t} \partial_{x}^{3})-6u \partial_{x}^{3}-6(uu_{tx}+uu_{t} \partial_{x})-3u_{x} \partial_{x}^{2}-3u_{x}u_{t} \right) v \\
&=\left( -4 \partial_{x}^{5}-4 u_{txxx}-12u_{txx} \partial_{x}-12u_{tx} \partial_{x}^{2}-4u_{t} \partial_{x}^{3}-6u \partial_{x}^{3}-6uu_{tx}-6uu_{t} \partial_{x}-3u_{x} \partial_{x}^{2}-3u_{x}u_{t} \right) v \\
&=-4v_{xxxxx}-4u_{txxx}v-12u_{txx}v_{x}-12u_{tx}v_{xx}-4u_{t}v_{xxx}-6uv_{xxx}-6uu_{tx}v-6uu_{t}v_{x}-3u_{x}v_{xx}-3u_{x}u_{t}v.
\end{align*}
How does that compare?
#### Ackbach
##### Indicium Physicus
Staff member
So, I think that $L= \partial_{x}^{2}+u_{t}$ is doomed, and here's why: there's no way you're going to get the resulting $u_{tt}$ to cancel from anything in the commutator. And the fact is, KdV is first-order in time. Therefore, that operator is incorrect.
You can see from my dissertation that the operators
\begin{align*}
L&=-\partial_{x}^{2}+u \\
M&=-4 \partial_{x}^{3}+3( \partial_{x} u+u \partial_{x})
\end{align*}
will work.
#### dwsmith
##### Well-known member
When I was doing some reading, I noticed the operator you used that is why I asked the question. I wasn't sure if I wrote it down wrong or if it would work.
#### dwsmith
##### Well-known member
Even when I use
\begin{align}
L &= \partial_{xx} + u\\
M &= -4\partial_{xxx} - 6u\partial_x - 3\partial_xu
\end{align}
the equations don't work out.
For $$[L,M]$$, I obtain:
$-6\partial_{xx}u\partial_x + u_{xxx} + 2u\partial_{xxx} - 6u^2\partial_x + 3u\partial_xu + 3\partial_xu\partial_{xx} + 3\partial_xu^2$
which simplifies to
$u_{xxx} - 6u_{xx}\partial_x - 9u_x\partial_{xx} + 9uu_x - u\partial_{xxx}$
Therefore, $$- 6u_{xx}\partial_x - 9u_x\partial_{xx} + 9uu_x - u\partial_{xxx}$$ has to equal $$6uu_x$$ some how.
#### dwsmith
##### Well-known member
Using these identities:
\begin{align}
\partial_{xxx}u &= u_{xxx} + 3u_{xx}\partial_x + 3u_x\partial_{xx} + u\partial_{xxx}\\
\partial_{xx}u\partial_x &= u_{xx}\partial_x + 2u_x\partial_{xx} + u\partial_{xxx}\\
u\partial_xu &= uu_x + u^2\partial_x\\
\partial_xu\partial_{xx} &= u_x\partial_{xx} + u\partial_{xxx}\\
\partial_xu^2 &= 2uu_x + u^2\partial_x
\end{align}
I re-wrote $$M$$ to see if it would help as
\begin{align}
L &= \partial_{xx} + u\\
M &= -4\partial_{xxx} - 6u\partial_x - 3\partial_xu
\end{align}
Then for $$LM$$ and $$-ML$$, I obtain:
\begin{align}
LM &= -4\partial_{xxxxx} - 6\partial_{xx}u\partial_x - 3\partial_{xxx}u - 4u\partial_{xxx} - 6u^2\partial_x - 3u\partial_xu\\
&= -4\partial_{xxxxx} - 15u_{xx}\partial_x - 21u_x\partial_{xx} - 6u\partial_{xxx} - 3u_{xxx} - 7u\partial_{xxx} - 9u^2\partial_x - 3uu_x\\
-ML &= 4\partial_{xxxxx} + 4\partial_{xxx}u + 6u\partial_{xxx} + 6u\partial_xu + 3\partial_xu\partial_{xx} + 3\partial_xu^2\\
&= 4\partial_{xxxxx} + 4u_{xxx} + 12u_{xx}\partial_x + 15u_x\partial_{xx} + 13u\partial_{xxx} + 12uu_x + 9u^2\partial_x\\
[L,M] &= u_{xxx} - 3u_{xx}\partial_x - 6u_x\partial_{xx} + 9uu_x
\end{align}
Where have I gone wrong? I have also done this with out writing $$3\partial_xu$$ but instead using $$3u_x$$ but leads no where as well.
Last edited:
#### dwsmith
##### Well-known member
Using these identities:
\begin{align}
\partial_{xxx}u &= u_{xxx} + 3u_{xx}\partial_x + 3u_x\partial_{xx} + u\partial_{xxx}\\
\partial_{xx}u\partial_x &= u_{xx}\partial_x + 2u_x\partial_{xx} + u\partial_{xxx}\\
u\partial_xu &= uu_x + u^2\partial_x\\
\partial_xu\partial_{xx} &= u_x\partial_{xx} + u\partial_{xxx}\\
\partial_xu^2 &= 2uu_x + u^2\partial_x
\end{align}
I re-wrote $$M$$ to see if it would help as
\begin{align}
L &= \partial_{xx} + u\\
M &= -4\partial_{xxx} - 6u\partial_x - 3\partial_xu
\end{align}
Then for $$LM$$ and $$-ML$$, I obtain:
\begin{align}
LM &= -4\partial_{xxxxx} - 6\partial_{xx}u\partial_x - 3\partial_{xxx}u - 4u\partial_{xxx} - 6u^2\partial_x - 3u\partial_xu\\
&= -4\partial_{xxxxx} - 15u_{xx}\partial_x - 21u_x\partial_{xx} - 6u\partial_{xxx} - 3u_{xxx} - 7u\partial_{xxx} - 9u^2\partial_x - 3uu_x\\
-ML &= 4\partial_{xxxxx} + 4\partial_{xxx}u + 6u\partial_{xxx} + 6u\partial_xu + 3\partial_xu\partial_{xx} + 3\partial_xu^2\\
&= 4\partial_{xxxxx} + 4u_{xxx} + 12u_{xx}\partial_x + 15u_x\partial_{xx} + 13u\partial_{xxx} + 12uu_x + 9u^2\partial_x\\
[L,M] &= u_{xxx} - 3u_{xx}\partial_x - 6u_x\partial_{xx} + 9uu_x
\end{align}
Where have I gone wrong? I have also done this with out writing $$3\partial_xu$$ but instead using $$3u_x$$ but leads no where as well.
I am not to sure about these derivative identities. On page number 10 or page 30 of the pdf, we have that
\begin{align}
LM &= -4\partial_{xxxxx} - \frac{5}{3}\alpha u\partial_{xxx} - \frac{5}{2}\alpha u_x\partial_{xx} - \frac{1}{6}\alpha^2u^2\partial_x - 2\alpha u_{xx}\partial_x - \frac{1}{12}\alpha^2uu_x - \frac{1}{2}\alpha u_{xxx}\\
-ML &= 4\partial_{xxxxx} + \frac{5}{3}\alpha u\partial_{xxx} + \frac{5}{2}\alpha u\partial_{xx} + \frac{1}{6}\alpha^2u^2\partial_x + 2\alpha u_{xx}\partial_x + \frac{1}{4}\alpha^2uu_x + \frac{2}{3}\alpha u_{xxx}
\end{align}
In my case, $$\alpha = 6$$. Using these identities, I obtain the desired results. I then compared the terms with using the previous method. The identities for $$\partial_{xxx}u$$ and $$u\partial_xu$$ add too many terms. The identity $$\partial_{xx}u\partial_x$$ is needed though. So those two identities either don't work for all $$\alpha$$ or there is an issue with them not sure what it is though.
Here is the link to the other document:
http://inside.mines.edu/~whereman/papers/Larue-MS-Thesis-2011.pdf
Last edited:
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# Seminar of Algebra
### Analysis of the DME post-quantum cryptosystem
Speaker:
Martin Avendano (Centro Universitario de la Defensa, Zaragoza)
Email:
avendano@unizar.es
Location:
Departamento de Álgebra
Date:
Thu, 13 jun 2019 11:00
The public-key cryptosystems (based on the difficulty of factoring integers) are vulnerable to the hypothetical quantum computer, whose realization seems imminent. Anyone that is currently storing communications ciphered with those cryptosystems will be able to decode them in the (near) future. The answer to such a problem led to what is called post-quantum cryptography, whose main goal is to develop public-key cryptosystems that can be used with classical computers and that are not vulnerable to attacks with quantum computers. The american agency NIST opened recently a contest asking for such cryptosystems, with the idea of selecting and then standarizing the best for global usage.
In this talk, I am going to present the DME cryptosystem, proposed by Prof. Ignacio Luengo (Univ. Complutense de Madrid) and implemented by Miguel Marco Buzunamiz and myself (Univ. de Zaragoza). This cryptosystem changes the integer factorization problem by the problem of factoring a polynomial map as the composition of three linear and two exponential maps. Compared to the standard RSA cryptosystem, the description of DME is significantly harder, but its implementation is competitive (both in key-size and running-time), which is one of the reasons the system attracted a lot of attention in the first round of the NIST contest. Although the system has not been broken in its more general form, we have found a weakness in the way certain maps are composed, which led to a structural attack that breaks the system (as submitted to NIST) in a few minutes. The attack reduces to the computation of the intersection of a toric variety with a linear space. If time allows, I will also present the main ideas of these algebraic attacks.
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# Notation for special summations
1. Aug 5, 2008
### epkid08
Is there special notation for a function like this:
$$g(x_1)=\sum^k_jf(x)$$
$$g(x_2)=\sum^p_k\sum^k_jf(x)$$
$$g(x_3)=\sum^s_p\sum^p_k\sum^k_jf(x)$$
If so, what would g(x_n) be?
2. Aug 5, 2008
### epkid08
I forgot to add, a function like this:
$$f(x_n)=\sum^{\sum^{\sum^{\sum^{\sum}}}}...$$
(the limit of each sum is another sum; fallowing the pattern in the above post of course)
3. Aug 5, 2008
### Ben Niehoff
For a small, finite number of indexes, sometimes I see the shorthand
$$\sum_{i,j,k} f(x)$$
This usually occurs when all of the indexes run from 0 to the same limit N.
If you have a variable number of indexes, then you can "index the indexes" as follows:
$$S_n = \sum_{i_1 \dots i_n} f(x)$$
Oh, wait, I see you want each index to run up to the previous index. For a small number of indexes, you can do
$$S_3 = \sum^N_{i > j > k} a_{ijk}(x)$$
And in general, you could probably write
$$S_n = \sum^N_{i_1 > \dots > i_n} a_{i_1 \dots i_n}(x)$$
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## graphs – Minimal coverage of the clique
How to solve the problem of the minimum coverage of the clique by using linear / full programming in a reasonable time?
Having an undirected graph, I try to partition all its vertices in cliques so that the number of cliques is as small as possible. The problem can be formulated as an entire program, where each vertex corresponds to an integer variable (index of its clique), and whose objective function is to minimize the sum of all these variables. For each edge do not in the graph, a condition is created to ensure that the corresponding vertex variables are not equal, like this:
$$b_k in {0, 1 }$$
$$x_i – x_j + M * b_k> = 1$$
$$x_j – x_i + M * (1-b_k)> = 1$$
$$b_k$$ indicates the relationship between the values of $$x_i$$ and $$x_j$$. With a big enough $$M$$one of the conditions is always true, in which case the other guarantees that the distance between the values is at least 1.
However, this approach seems to have an exponential complexity, operating only on very small graphs.
Assuming that the number of cliques should be reduced and there is usually no border between the cliques, is there a better approach to this problem? I think first of all to find the maximum independent group and use it to correct some variables (because it is guaranteed that they belong to different cliques). Will it help to increase speed?
## graphs – Algorithm to generate random incrementing numbers up to a limit
I'm trying to write code to generate incremental sequences of numbers such as:
``````0 + 1 + 3 + 5 + 1 = 9
0 + 5 + 1 + 1 + 1 = 8
0 + 1 + 1 + 2 + 1 = 5
``````
I have 3 constraints:
1) I need to have a limited number of addends (here it is `= 5`)
2) the final sum must be less than a certain limit (the limit is here `<9`)
For now, I generate sequences randomly and selects only those that are appropriate. For 2-digit numbers and for long sequences (`> 8`) my algorithm takes a lot of time.
At least can you tell me that the CS branch is studying such problems?
## "Mobility" in graphs – Mathematics Stack Exchange
Let $$G$$ to be a graph on $$n$$ the tops, $$D$$ a subset of vertices. We interpret $$D$$ like a pebble pattern on $$G$$. A summit $$v$$ of $$G$$ is occupied if it is in $$D$$, unoccupied other. A move take a pebble from a busy top and move it to an adjacent unoccupied vertex.
the mobility of $$D$$, noted by $$m (D)$$ is the number of possible moves. the $$k$$-mobility of $$G$$, noted by $$m_k (G)$$ is the maximum mobility of any vertex-sized subset $$k$$. Mobility of $$G$$, noted by $$m (G)$$, is the maximum mobility of any subset of vertices. (Btw, do these concepts have official names, are they studied?)
It's easy to show that $$m_k (G)$$ is symmetrical on the segment $$[0,n]$$. It's also easy to show that $$m (G)$$ is equal to the number of edges of a larger subgraph covering two parts.
I'm interested in one aspect of the behavior of $$m_k (G)$$ (for fixed $$G$$). Let $$m = lfloor frac n2 rfloor$$. The question is: is $$m_k (G)$$ weakly unimodal on the segment $$[0,m]$$in other words, is there an index $$t$$ such as $$m_ {i-1} (G) leq m_i (G)$$ for $$i leq t$$ and $$m_ {i + 1} (G) geq m_i (G)$$ for $$i geq t$$. A proof (or a counter-example) of the trees would already help a lot.
Some partial results (for trees and on the segment $$[0,m]$$):
1. It is easy to find an example where the function becomes stationary, then increases further.
2. Computers running on small random trees did not produce counter-examples.
3. If the function decreases, it decreases exactly $$1$$ (my proof is not quite trivial).
4. A local maximum can be anywhere, for star charts this is at $$i = 1$$, for cycles it's a $$i = m$$.
## Upper bound of the length of the cycles without chord in the d-regular graphs
Given a $$d$$regular graph with $$n$$ is there a known upper limit (not trivial) on the length of cycles without strings (presumably $$d$$ and $$n$$)? I did not find anything after some online research. Thank you.
## graphs and networks – Express an Edge list as a 0-1 table with headers
Consider the edges
`edges = {S1040 [DirectedEdge]F283, S1197[DirectedEdge]F243, S1197[DirectedEdge]F245, S1863[DirectedEdge]F243, S1863[DirectedEdge]F245, S1863[DirectedEdge]F283, S1863[DirectedEdge]F244, S1863[DirectedEdge]F246, S1863[DirectedEdge]F247, S1863[DirectedEdge]F280, S1863 [DirectedEdge]F281, S1863[DirectedEdge]F282, S1863[DirectedEdge]F284, S2174[DirectedEdge]F243, S2174[DirectedEdge]F280, S2174[DirectedEdge]F281, S2174[DirectedEdge]F284, S2325[DirectedEdge]F247, S2340[DirectedEdge]F245, S2344[DirectedEdge]F282}`
How can I create an adjacency matrix from this chart as a table where the lines are the Fxxx nodes and the columns are the Syyyy nodes and where the rows and columns are in ascending order . For example, line 1 corresponds to F243, line 2 to F244, and so on. Similarly, column 1 corresponds to S1040, column 2 to S1197, and so on.
## data – How to design the best UX for Graphs?
#### Battery Exchange Network
The Stack Exchange network includes 175 question-and-answer communities, including Stack Overflow, the largest and most reliable online community on which developers can learn, share knowledge and build their careers.
Visit Stack Exchange
## graphs and networks – Grouping of edge points of an image?
Consider the following picture
I want to group the points obtained after the detection of the contours, then, later, to color the contour points.
My attempt:
``````img = URLExecute["https://i.stack.imgur.com/4q309.png"];
edgeImg = img // EdgeDetect;
edgePoints = PixelValuePositions[edgeImg, 1];
clusteredEdgePoints = FindClusters[edgePoints, Method -> "NeighborhoodContraction"];
{edgeImg, Graphics[{ColorData["DarkRainbow"][RandomReal[]], Line[#]} & / @
clusteredEdgePoints]}
``````
{, }
Question:
We can see, `FindClusters` did not group the internal and external ellipses. How should I say `FindClusters` to group internal and external ellipses? or is there another alternative?
Note: I would like the question to be as general as possible, that is, I would not want to enter the number of clusters explicitly.
Some other pictures may be as follows:
``````img1 = URLExecute["https://i.stack.imgur.com/Z150N.png"];
img2 = URLExecute["https://i.stack.imgur.com/spkHI.png"];
``````
,
## graphs – Optimization of the algorithm of De Boor & # 39; s
According to the De Boor algorithm, a basic B-Spline function can be evaluated using the formula:
$$B_ {i, 0} = left { begin {array} {ll} 1 & mbox {if} t_i the x
$$B_ {i, p} = frac {x-t_i} {t_ {i + p} -t_i} B_ {i-1, p} (x) + frac {t + {i + p + 1} – x} {t_ {i + p + 1} -t_ {i + 1}} B_ {i + 1, p-1} (x)$$
where the function $$B$$ is defined for $$n$$ checkpoints for the degree curve $$d$$. The domain $$t$$ is divided into $$n + d + 1$$ points called nodes (in the node vector). To evaluate this, we can define a recursive function $$B (i, p)$$.
B-Spline itself is represented by:
$$S (x) = sum {c_iB_ {i, p}}$$.
To evaluate this, Wikipedia's algorithm tells us to take $$p + 1$$ checkpoints from $$c_ {k-p}$$ at $$c_p$$and then repeatedly take the weighted average of each consecutive pair, eventually reducing it to one point.
I find this algorithm very good for one or two evaluations; However, when we draw a curve, we take hundreds of points in the curve and connect them to make it smooth. The recursive formula still requires up to $$(p-1) + (p-2) + (p-3) …$$ calculations, no? (To take the weighted averages)
In my research, however, we need to evaluate only one polynomial – because B-Spline is ultimately composed of $$p + d + 1$$ basic polynomials (as I will show).
Suppose we take a node vector $$[0, .33, .67, 1]$$ and checkpoints $$[0, 1, 0]$$ (diploma $$1$$), we can then represent the basic polynomials in the form:
$$c_0B_ {0,1} = 0, mbox {if} 0 leq x <.25, + 0, mbox {if} .25 leq x <.5$$
$$c_1B_ {1,1} = 4x-1, mbox {si} .25 leq x <.5, + , , – 4x + 3, mbox {si} .5 leq x <.75$$
$$c_2B_ {2,1} = 0, mbox {if} .5 leq x <0,75 + 0, mbox {if} .75 leq x <1$$
Now we can flatten that they produce:
$$S (x) = sum {c_i B_ {i, 1}} = left { begin {array} {ll} 0 & mbox {if} 0 the x <.25 \ 4x-1 & mbox {if} .25 the x <.5 \ -4x + 3 & mbox {if} .5 the x <.5 \ 0 & mbox {if} .75 the x <1 \ end {array} right.$$
Now, if we were to calculate $$S$$ to no matter $$x$$, we can directly deduce which polynomial to use and then calculate it $$d$$ multiplications and $$d + 1$$ additions.
I've implemented this calculation explicitly using `Polynomial` objects in JavaScript. See https://cs-numerical-analysis.github.io/.
Source: https://github.com/cs-numerical-analysis/cs-numerical-analysis.github.io/blob/master/src/graphs/BSpline.js
I want to know why people do not use the algorithm that I have described. If you calculated the polynomial representation of B-Spline then flatten outside, it will be a one-time cost. Should not this one-time cost be offset by removing the unnecessary recursive average?
## graphs and networks – Maintaining associative bracketing in place
The following Mathematica code displays the vertices of a given graph after the conversion of an expression into an appropriate format (using both tensor and parallel notation headers.) Labels are displayed at the vertex level, but the associative rules are How can I avoid this? (ie, how do I keep square brackets when vertices are displayed?
``````DiplayGraph[g_] : =
With[{vlist = VertexList[g]}
Graphic[g, VertexLabels ->
vlist -> Map[# /. {ExpProduct -> (ToString[
HoldForm[CircleTimes[##]]]&)
Parallel -> (ToString[
HoldForm[DoubleVerticalBar[##]]]&)} &, vlist]],
EdgeLabelStyle -> Directive[10, Background -> White],
VertexLabelStyle -> Directive[10, Background -> White]]]
``````
When running this code on a graph:
``````DisplayGraph[Graph[{A[1, 2] -> B[2, B[3, 4]]}]]
``````
the following output is generated:
I would like 2 || 3 || 4 to appear as 2 || (3 || 4) consistent with parentheses in B[2, B[3, 4]](that is, I do not want associative deletion of parentheses). Which command can be inserted to ensure this?
## graphs – Rebuilt the shortest path from a list of predecessors
I'm trying to make a shortest path reconstruction with the given parameters:
• a table P, which contains the predecessors of each vertex on the shortest path from S to I
• a starting vertex S, defined by a P[S] = -1
• the end of the summit T, which is the destination of the shortest path I am trying to reconstruct
My idea was to start at the end of the table, find the predecessor of the T-summit, and continue looking for the predecessors of the predecessors until I was at the starting point S. Is my solution correct? Thank you!
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# Mathematical Expression
I want to display the following in my thesis document: (1/7) ≤ X < (6/7)
I tried using the command: $\frac{1}{7}$ \leq $X <$\frac{6}{7}$ But I keep getting error messages, such as "missing$ inserted" appointing to the part $\frac{1}{7}$ \leq.
Though it does print out what I want, but it still seems to be wrong somehow. And there is some white space missing between ≤ and X.
Neither $[$\frac{1}{7}$] \leq$X
nor $($\frac{1}{7}$) \leq$X
nor ${$\frac{1}{7}$} \leq$X
nor \frac{1}{7}$\leq$X
were correct.
• remove all the $ except one at the start and one at the end, this is a single math expression. Sep 13 '21 at 11:42 • Welcome to TeX SX! You don't have use a pair of$ $for each part of the formula. Just use $\frac{1}{7} \leq X < \frac{6}{7}$. Sep 13 '21 at 11:43 • Thanks so much! That helped, much appreciated! :) Sep 13 '21 at 11:44 • Rewelcome :-)..I suggest to read this link also: tex.meta.stackexchange.com/questions/228/… Sep 13 '21 at 12:02 • @Sebastiano Very helpful link, thank you! Sep 13 '21 at 12:44 ## 1 Answer Your problem is that the \leq should be inside the math formula, not outside. Try this: $\frac{1}{7} \leq X < \frac{6}{7}\$
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# If limit of f(x)=27 as x->c, what the limit of (f(x))^(3/2) as x->c?
###### Question:
If limit of f(x)=27 as x->c, what the limit of (f(x))^(3/2) as x->c?
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##### Quesuion 10Among 20 golden _ hamster litters recorded, there was sample mean of 1 7.72 baby hamsters. with sample standard deviation of _ =2.5 hamsters per liter: Create 95%0 confidence interval for the mean number of baby hamsters per liter:07.73+ 1.0957b) 07.72 1.170007.72 _ 0.559007.72 + 0.966607.72 + 2.50ONone of the above
Quesuion 10 Among 20 golden _ hamster litters recorded, there was sample mean of 1 7.72 baby hamsters. with sample standard deviation of _ =2.5 hamsters per liter: Create 95%0 confidence interval for the mean number of baby hamsters per liter: 07.73+ 1.0957 b) 07.72 1.1700 07.72 _ 0.5590 07.72 + 0.9...
##### A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation....
A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation. y" -y= 11t, y(t) = - 110 The general solution is y(t) = (Do not used, D, e, E, I, or I as arbitrary constants since these letters already have defined meanings.)...
##### Block (m = 1 kg) is placed on a spring (K = 900 Nlm) which is compressed 0.1 m.m=VI -77K = 900 N/m X-O1mhs4mdx = ?77What is the velocity of the mass once the spring is released? b. If the mass is on a surface that is m high; what is the horizontal displacement of the mass when it hits the ground?
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##### In the mechanism for electrophilic aromatic substitution with a diazonium ion as the electrophile, why does nucleophilic attack occur on the terminal nitrogen of the diazonium ion rather than on the nitrogen that has the formal positive charge?
In the mechanism for electrophilic aromatic substitution with a diazonium ion as the electrophile, why does nucleophilic attack occur on the terminal nitrogen of the diazonium ion rather than on the nitrogen that has the formal positive charge?...
##### [Review Topica] [Relerences] Use the References access important Falues if nceded for this question Does reaction occur when aqueous solutions of barium nitrate and iron(IIl) sulfate are combined? yesIfa reaction does Occur, write the net ionic equationUse the solubility Tules prorided in the OWL Preparation Paze determine the solubility of cempounds. Use the pull-down boxes to specify states such &5 (0q) or (9). box needed leave blank:Subinit AnstARebry Elire Ghoummoro (romp attrinpts
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##### A Venn diagram Question 2 and R given below;1 1 4U answei [email protected]
A Venn diagram Question 2 and R given below; 1 1 4U answei [email protected] 10...
##### What is the simplest radical form of the sqrt10?
What is the simplest radical form of the sqrt10#?...
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# 12.2 Surface Area of Prisms & Cylinders
## Presentation on theme: "12.2 Surface Area of Prisms & Cylinders"— Presentation transcript:
12.2 Surface Area of Prisms & Cylinders
Definitions Prism – polyhedron with 2 faces (called bases) that lie in planes. Named by the shape of the bases. Lateral Faces – the faces that are NOT bases (all are ’ogram shaped) Lateral Edges – edges of the lateral faces that are NOT edges of the bases as well. Height (altitude) - distance between the bases. Right Prism – lateral edges are to bases. Oblique Prism – lateral edges are NOT to the bases. (looks slanted)
Right Oblique Triangular Prisms Bases (2 Δs)
Lateral faces (3 ll’ograms) height Lateral edges (3) Triangular Prisms
3-D Areas Lateral Area (LA) – the sum of the areas of the lateral faces only. Does not include the area of the bases. Surface Area (S) – the sum of the areas of ALL the faces. Lateral area + area of the bases
Net Defn. – a 2-dimensional representation of a solid.
Just think “unfold” the figure and lie it flat. Ex:
To find surface or lateral areas, you could find the areas of each individual face and then add them all together; OR you could use formulas! Thm 12.2 – SA of a rt. Prism SA = 2B + Ph B = area of base, P = perimeter of base, h = height of prism What about Lateral Area? * remember: LA is everything BUT the bases! So, LA = Ph
Ex: Find the lateral & surface areas of the triangular prism.
6 in. 60o 10 in.
Cylinder Defn. – solid with , circular bases.
Can be right or oblique. Lateral Area – the area of the curved surface. What does the curved surface look like if lied out flat? Think of the label of a soup can! It’s a rectangle! (area of rectangle = bh) Surface Area – lateral area + area of bases. h h
Let’s look at lateral area 1st! So, SA = 2B + Circumference × h
Thm 12.3: SA of a rt. cylinder Let’s look at lateral area 1st! LA = Circumference × h or LA = 2rh So, SA = 2B + Circumference × h SA = 2r2 + 2rh
Ex: Find the lateral & surface areas of the cylinder.
LA = 2rh LA = 2(4)(8) LA = 64 m2 SA = 2r2 + 2rh SA = 2(42) + 64 SA = 32 + 64 SA = 96 m2 4 m. 8 m.
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