text:
Algebra; Functions & Graphs

Given:

Why is -2 non-inclusive?

-

The derivative of the function (the slope) is 0 at x = -2.

The definition of an increasing function requires that the slope be strictly positive. :)

-
I presume you mean strictly increasing and are talking about continuously differentiable functions. Then if the slope is positive, it's true that $f$ is strictly increasing, but not the converse; consider $f(x)=x^3$. –  Michael Hoppe Feb 28 at 13:32
This is not correct. –  Mark McClure Feb 28 at 14:16
@MarkMcClure Do you mind to explain my error? –  Michael Hoppe Feb 28 at 14:25
@MichaelHoppe I mean this answer is incorrect - yours is the correct one! I even upvoted it! –  Mark McClure Feb 28 at 14:35
@MarkMcClure thanks for clarification. –  Michael Hoppe Feb 28 at 14:39

The function is strictly increasing on any interval $J\subset(-\infty,-2]$, so the suggested answer is true since $(-\infty,-2)\subset(-\infty,-2]$.

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This is correct. –  Mark McClure Feb 28 at 14:15

format: plain


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Apache Arrow 是 Apache 基金会全新孵化的一个顶级项目。它设计的目的在于作为一个跨平台的数据层，来加快大数据分析项目的运行速度。

## arrow的python版本安装

arrow是apache下的一个顶级项目，它是一个跨平台的内存数据交换格式。通过conda来进行安装：conda install -c conda-forge pyarrow，官方的安装推荐使用conda，具体可以见apache arrow documentation.

<pyarrow.lib.Buffer at 0x7f46706d0ab0>

### 结合numpy使用

<pyarrow.lib.DoubleArray object at 0x7f467b68aea8>
[
0.688175,
0.979032,
0.91343,
0.725985,
0.469235,
0.373089,
0.792048,
0.472252,
0.615361,
0.693604,
...
0.240511,
0.162609,
0.518071,
0.816558,
0.736163,
0.509702,
0.914533,
0.879404,
0.979877,
0.883003
]

### 结合pandas使用

['_column',
'_validate',
'append_column',
'cast',
'column',
'columns',
'drop',
'equals',
'flatten',
'from_arrays',
'from_batches',
'from_pandas',
'itercolumns',
'num_columns',
'num_rows',
'remove_column',
'schema',
'set_column',
'shape',
'to_batches',
'to_pandas',
'to_pydict']

### 导入csv格式的数据

26 ms ± 97.9 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

164 ms ± 1.18 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

## arrow的IO操作

934 µs ± 23.3 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)
969 µs ± 88 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

8.76 µs ± 24.3 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
5.73 µs ± 9.02 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
8.26 µs ± 28.8 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)

## pickle和arrow的对比

207 µs ± 1.78 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

200 ms ± 5.59 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)
206 ms ± 7.8 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

4.72 ms ± 18.9 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)
12.4 ms ± 42.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)


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# Peacefully yours...!!!

Geometry Level 1

We see the $$Yin-Yang$$ sign as a philosophical symbol. So, Sara, on the occasion of a cultural event in her school, decided to paint the entire symbol on a really large canvas. Sara goes to the market to buy the required amount of paint (we can assume that she only does the black paint work, and leaves the white part as it is). Sara is confused about the minimum amount of money she should carry along with her. It is your task to help Sara calculate the minimum amount (in $$dollars$$). It costs $$12$$ $$dollars$$ to paint an area of $$1$$ $$square meter$$ on the canvas and the radius of the entire sign is $$7$$ $$meters$$. Assume all curvatures to be equal.)

×

Problem Loading...

Note Loading...

Set Loading...


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Processing integral forged connecting rod by CNC

Processing integral forged connecting rod by CNC

Summary

The overall forged connecting rod and the overall shape of the connecting rod are formed by the CNC machine tool at one time.

Details

The overall forged connecting rod and the overall shape of the connecting rod are formed by the CNC machine tool at one time, the excessive arc of the connecting rod is smooth, and the stress concentration is reduced; the shortcomings of the conventional arc cutting in the forming and forming are changed, and the arc cutting makes the periphery of the connecting rod body due to high temperature gold.

The phase structure changes, and the residual stress increases sharply, which weakens the strength of the connecting rod.


text:
# Ex.3.4 Q2 Understanding Quadrilaterals Solution - NCERT Maths Class 8

Go back to  'Ex.3.4'

## Question

Identify all the quadrilaterals that have.

(a) four sides of equal length

(b) four right angles

## Text Solution

Steps:

a) Four sides of equal length - Rhombus and Square are the quadrilaterals with $$4$$ sides of equal length.

b) Four right angles - Square and Rectangle are the quadrilaterals with $$4$$ right angles.

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school


text:
# Is TripleDES 168bit vulnerable to Differential Cryptanalysis?

I was reading this paper. In the table-1 of the paper it says TripleDES (showing both 128bit and 168bit keysize) is vulnerable to Differential Cryptanalysis. It also says that AES (showing all three keysize) is strong against Differential Cryptanalysis. If AES-128bit is secure against Differential Cryptanalysis then why not TripleDES-168bit as well?

So, is it the paper that the authors haven't made it clear or is it true that TripleDES 168bit keysize is vulnerable to Differential Cryptanalysis attack?

-
The question is valid, but if that's a scientific paper then I'm little red riding hood. –  Maarten Bodewes Jul 18 '14 at 11:54
One should not trust a table/paper where the time to enumerate all 56-bit DES key is given as 400 days at a rate intended to be realistic (the EFF cracker did that in few days in 1998).. and where for 112-bit 2keys-3DES, all other things being equal, the time is only twice that!! $\;$ –  fgrieu Jul 18 '14 at 13:07
@owlstead: Agreed. Not only is it full of both factual and grammatical errors, but most of the text, or at least the more fluent parts of it, appears to be plagiarized. If this were an undergrad course assignment, I'd give it an F; since the authors appear to be grad students, and since it appears to have been published in something pretending to be a scientific journal... –  Ilmari Karonen Jul 18 '14 at 15:31
@e-sushi, may be its because they are written in uppercase instead of lowercase. Using the uppercase address I also found 404 error. –  Giliweed Jul 18 '14 at 16:35
@Giliweed Darn, I would’ve expected Google to rewrite such URLs accordingly. My mistake… thanks for the heads-up on that! Much appreciated. (Removed my related comment to avoid confusion.) –  e-sushi Jul 18 '14 at 16:37

This claim is bogus. DES itself has a 13-round differential with probability around $2^{-47}$, so TripleDES with its 48 rounds is resistant to any sort of differential attack.


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## Tricky integration by parts

Can anyone show me how to integrate:

[(n+1)*(x^n)]*[1+x+(x^(x+1))+(x^(x+1)^(x+2))+(x^(x+1)^(x+2)^(x+3) )] over [0,1]?

Thanks!

I know I'm supposed to do it twice but I'm not sure what to take as u and dv (I'm assuming I should take the big messy one as u and the first nicer one as dv, but even still I'm having trouble).

Edit: Integrate with respect to x (not n, but I guess that's obvious).


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Free Version
Easy

# Interpreting $K_{eq}$ values

SATCHM-ZNKNKK

If the $K_{eq}$ for a reversible reaction is slightly less than 1, which of the following statements is true?

A

The formation of products is slightly favored.

B

The formation of products is greatly favored.

C

The formation of reactants is slightly favored.

D

The formation of reactants is greatly favored.

E

Neither the formation of reactants nor products is favored.


text:
# GFM

##### Sections
You are here: Home On the mean curvature of the periodic surfaces of revolution

# On the mean curvature of the periodic surfaces of revolution

GFM seminar
IIIUL, B1-01
2010-05-11 14:30 .. 15:30
Add event to calendar:   vCal    iCal

by Katsuei Kenmotsu (Mathematical Institute, Tohoku University, Sendai, Japão)

A surface of revolution in the Euclidean space is determined by the mean curvature. In this talk, a necessary and sufficient condition for such a surface to be periodic is given in terms of the mean curvature. This extends the famous result by Delaunay (1841) for constant mean curvature surfaces of revolution. First, we discuss with two dimensional case, and then the higher dimensional case, separately.


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# Cute trigonometric triviality

For which values of the coefficient $c$ does the quantity $$\cos\alpha\cos\beta- c\sin\alpha\sin\beta$$ depend on $\alpha$ and $\beta$ only through their sum?

(I'll post a quick answer below. This will be the first time I've posted a question with intent to immediately post an answer.)

-

We want $f(\alpha, \beta) = g(\alpha + \beta)$. This means that $f(\alpha,-\alpha) = g(0) = f(0,0)$, $\forall \alpha$.

$f(\alpha,-\alpha) = f(0,0)$ for all $\alpha$. Hence, we get that $$\cos^2(\alpha) + c \, \sin^2(\alpha) = 1, \, \, \forall \alpha$$ $$c \, \sin^2(\alpha) = \sin^2(\alpha), \, \, \forall \alpha$$ Hence, $c = 1$.

-

Well, let's define the new quantities $s=\frac{\alpha+\beta}{2}$ and $d=\frac{\alpha-\beta}{2}$. With those quantities the expression reads $$E:=\cos(s+d)\cos(s-d)-c\sin(s+d)\sin(s-d).$$ The question now is: For which values of $c$ is this expression independent from $d$?

Let's apply the standard addition theorems to get $$E =(\sin s\cos d+\cos s\sin d)(\sin s\cos d-\cos s\sin d) -c(\cos s\cos d-\sin s\sin d)(\cos s\cos d+\sin s\sin d).$$

Using $(a+b)(a-b) = a^2-b^2$, we therefore get $$E=\sin^2 s\,\cos^2 d-\cos^2s\, \sin^2d - c(\cos^2 s\,\cos^2 d-\sin^2 s\,\sin^2 d).$$

Now we collect the functions of $s$ to get $$E = \sin^2 s(\cos^2 d+c\,\sin^2 d) - \cos^2s(\sin^2 d+c\,\cos^2 d).$$

Now it is easy to see that the only possibility that $E$ is independent from $d$ (and therefore in the original form depends only on the sum) is $c=1$, where $\sin^2 d+\cos^2d=1$

-

Let $f(\alpha,\beta) = \cos\alpha\cos\beta- c\sin\alpha\sin\beta$. Since this depends on $\alpha$ and $\beta$ only through their sum we have

$$f(\alpha,\beta)=f(\alpha+\beta,0).$$

Then

$$f(\alpha+\beta,0) = \cos(\alpha+\beta)\cos 0 - c\sin(\alpha+\beta)\sin 0 = \cos(\alpha+\beta).$$

So by the usual identity, $c=1$.

Later edit: Another way would be to write \begin{align} \cos\alpha\cos\beta - c\sin\alpha\sin\beta & = \Big(\cos\alpha\cos\beta - \sin\alpha\sin\beta\Big) - (1-c)\sin\alpha\sin\beta \\[8pt] & = \cos(\alpha+\beta) - (1-c)\sin\alpha\sin\beta \end{align} and then observe that the last term doesn't depend on $\alpha$ and $\beta$ only through their sum. From one point of view, this seems like the obvious way to do it---far more so than what I did above, and yet what I did above seems simpler.

-
Well, this is clear when $c=1$, but what about otherwise? –  Cameron Buie Jul 4 '12 at 17:51
@CameronBuie : If it depends on $\alpha$ and $\beta$ only through their sum, then the identity I wrote above holds, and that simplifies to $\cos(\alpha+\beta)$. Apply the usual identity and get $c=1$. So in other words, it works ONLY if $c=1$. –  Michael Hardy Jul 4 '12 at 17:56
@MichaelHardy: I'm almost tempted to downvote, because I think the way you've written the answer that's not clear at all. –  Ben Millwood Jul 4 '12 at 18:23
@BenMillwood : OK, I've expanded on it. –  Michael Hardy Jul 4 '12 at 19:30


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# Neutralisation question on the equation

#### lukemt11

I was just having a look at this reaction and couldn't work out the equation, can anyone help me out?
HSO4 + NaOH <--> Na2SO4 + H2O

Last edited:


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mechanics physics example

\label{13.8.3}\], $-m_{1}(\ddot{x}+\ddot{y})+m_{2}(\ddot{x}+\ddot{y})=-g(m_{1}-m_{2}) \label{13.8.4}$. It is intended to be interactive and to require students to process results, perform calculations and solve problems. The Wet Surface feature is used to implement the source term for the water vapor and to ... En Savoir Plus. This is a multiphysics model because it involves fluid dynamics coupled with heat transfer. Search within a range of numbers Put .. between two numbers. Apply Lagrange’s equation (13.4.13) in turn to the coordinates $$x$$ and $$y$$: $M\ddot{x}+m_{1}(\ddot{x}+\ddot{y})+m_{2}(\ddot{x}+\ddot{y})=-g(M-m_{1}-m_{2}). The rest is up to you. * Modeling thermal expansion Example $$\PageIndex{5}$$ Another example suitable for lagrangian methods is given as problem number 11 in Appendix A of these notes. The speed of the mass $$m_{2}$$ is therefore $$\dot{x}+\dot{y}$$ in laboratory space. example, the measurement of velocity, whose (derived) units uses the (fundamen-tal) units of length and time. The constant is equal to whatever the initial value of the left hand side was. \label{13.8.19}$. En Savoir Plus, This model refers to a portion of the vascular system of a young child - the upper part of the aorta artery.

It is at the end not of the usual inflexible string, but of an elastic spring obeying Hooke’s law, of force constant $$k$$. The resultant speed is the orthogonal sum of these.

The aim here is to cover many different types of problems, from easy to difficult, to help you study and prepare more effectively. It illustrates how fluid flow can deform solid structures and how to solve for the flow in a continuously deforming geometry. Now we can easily eliminate $$\dot{\phi}$$ between Equations $$\ref{13.8.10}$$ and $$\ref{13.8.11}$$, to obtain a single equation relating $$\dot{\theta}$$ and $$\theta$$: $b\dot{\theta}^{2}(1+c\sin^{2}\theta)-d\cos\theta-1=0, \label{13.8.12}$, $b=\frac{Mma^{2}}{(2M+m)E},\quad c=\frac{m}{2M},\quad d=\frac{mga}{E}=-\sec\alpha. Both pulleys rotate freely without friction about their axles. These, then, are two differential equations in the two variables. * The fundamentals: static linear analysis A pearl of mass $$m$$ slides smoothly around inside the torus. Mechanics can be divided into 2 areas - kinematics, dealing with describing motions, and dynamics, dealing with the causes of motion. \label{13.8.11}$. The kinetic energy of the torus is the sum of its translational and rotational kinetic energies: $$\frac{1}{2}M(a\dot{\phi})+\frac{1}{2}(Ma^{2})\dot{\phi}^{2}=Ma^{2}\dot{\phi}^{2}$$, $$\frac{1}{2}ma^{2}(\dot{\theta}^{2}+\dot{\phi}^{2}-2\dot{\theta}\dot{\phi}\cos\theta)$$, \[ T=Ma^{2}\dot{\phi}^{2}+\frac{1}{2}ma^{2}(\dot{\theta}^{2}+\dot{\phi}^{2}-2\dot{\theta}\dot{\phi}\cos\theta). It is easy to eliminate $$\ddot{\phi}$$ and hence get a single differential equation in $$\theta$$:. These two equations can be solved at one’s leisure for $$\ddot{x}$$ and $$\ddot{y}$$. Ce site web utilise des cookies pour fonctionner et améliorer votre expérience. The torus is rolling at angular speed $$\dot{\phi}$$, If you are good at differential equations, you might be able to do something with this, and get $$\theta$$ as a function of the time. This will be very useful when studying for tests and exams. The unstretched natural length of the spring is $$l$$, and, as shown, its extension is $$r$$. Sign up below to receive insightful \[ (2M+m\sin^{2}\theta)a\ddot{\theta}+ma\sin\theta\cos\theta\dot{\theta}^{2}+(2M+m)g\sin\theta=0. unsubscribe at any time. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. Jeremy Tatum (University of Victoria, Canada).

.

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# Forum

In Figure, if AC = ...

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# In Figure, if AC = BD, then prove that AB = CD.

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In Figure, if AC = BD, then prove that AB = CD.

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It is given, AC = BD

From the given figure, we get,

AC = AB + BC

BD = BC + CD

⇒ AB + BC = BC + CD [AC = BD, given]

We know that, according to Euclid’s axiom, when equals are subtracted from equals, remainders are also equal.

Subtracting BC from the L.H.S and R.H.S of the equation AB + BC = BC + CD, we get,

AB + BC - BC = BC + CD - BC

AB = CD

Hence Proved.

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On January 13, the SpaceX Transporter-3 mission launched many small satellites into a 540 km sun-synchronous orbit. Among these satellites were DELFI-PQ, a 3U PocketQube from TU Delft (Netherlands), which will serve for education and research, and EASAT-2 and HADES, two 1.5U PocketQubes from AMSAT-EA (Spain), which have FM repeaters for amateur radio. The three satellites were deployed close together with an Albapod deployer from Alba orbital.

While DELFI-PQ worked well, neither AMSAT-EA nor other amateur operators were able to receive signals from EASAT-2 or HADES during the first days after launch. Because of this, I decided to help AMSAT-EA and use some antennas from the Allen Telescope Array over the weekend to observe these satellites and try to find more information about their health status. I conducted an observation on Saturday 15 and another on Sunday 16, both during daytime passes. Fortunately, I was able to detect EASAT-2 and HADES in both observations. AMSAT-EA could decode some telemetry from EASAT-2 using the recordings of these observations, although the signals from HADES were too weak to be decoded. After my ATA observations, some amateur operators having sensitive stations have reported receiving weak signals from EASAT-2.

AMSAT-EA suspects that the antennas of their satellites haven’t been able to deploy, and this is what causes the signals to be much weaker than expected. However, it is not trivial to see what is exactly the status of the antennas and whether this is the only failure that has happened to the RF transmitter.

Readers are probably familiar with the concept of telemetry, which involves sensing several parameters on board the spacecraft and sending this data with a digital RF signal. A related concept is radiometry, where the physical properties of the RF signal, such as its power, frequency (including Doppler) and polarization, are directly used to measure parameters of the spacecraft. Here I will perform a radiometric analysis of the recordings I did with the ATA.

## List of RF recordings

Happy New Year! To celebrate, I have put together a list of RF recordings. Over the last few years, and specially since the start of the collaboration between GNU Radio and SETI Institute, I have been publishing a number of RF recordings in Zenodo. The search function of Zenodo is not very good, and I thought that readers of this blog would find useful to have a list of all the recordings I have published. The list of recordings can be accessed here and in the website menu, under “Publications“.

I have also published an excerpt of the recording of James Webb Space Telescope that I did on December 26. This is just the first 25 minutes of the recording, so that both polarizations fit into maximum 50 GB of a Zenodo dataset. The sample rate is still 3.84 Msps, so the sequential ranging tones are present in these files. The dataset is called “James Webb Space Telescope S-band recording with Allen Telescope Array (wideband excerpt)“. In some days I will also publish a decimated version (containing the telemetry but not the ranging tones) of the full recording.

Update 2022-01-03: I have now published the full recording decimated to 320 ksps. This is available in the dataset “James Webb Space Telescope S-band recording with Allen Telescope Array (320 kHz bandwidth)“.

Published
Categorised as Events

## JWST sequential ranging

In my last post I spoke about the James Webb Space Telescope telemetry, and I decoded a recording I made with the Allen Telescope Array. I used an IQ sample rate of 3.84 Msps when doing this recording because I wanted to see if there were any ranging signals. Usually, ranging signals have a bandwidth of 1.5 MHz or less in baseband, so after phase modulation, approximately 3 MHz are used. Thus, 3.84 Msps gives enough bandwidth to record the typical ranging signals.

After looking at the waterfall of the recording carefully, I saw that there are sequential ranging signals present almost all the time. This is expected. Since the recording was done 7 hours after the first correction manoeuvre, the DSN would be doing ranging to compute accurate ephemerides. Often, ranging signals are not used every time that a spacecraft is tracked, but only when the ephemerides need to be refined, such as when planning a manoeuvre or shortly after executing one.

In this post I analyse these sequential ranging signals. I still haven’t had time to publish the recordings in Zenodo. After seeing that the wideband recording is of interest, due to the presence of these signals, I’m planning to publish a shorter segment of the wideband recording (the full recording is 241 GB per polarization) and publish a decimated version of the full recording where only around 100 kHz of spectrum are present (which is enough for the telemetry signal).

## Decoding James Webb Space Telescope

The James Webb Space Telescope probably needs no introduction, since it is perhaps the most important and well-known mission of the last years. It was launched on Christmas day from Kourou, French Guiana, into a direct transfer orbit to the Sun-Earth L2 Lagrange point. JWST uses S-band at 2270.5 MHz to transmit telemetry. The science data will be transmitted in K-band at 25.9 GHz, with a rate of up to 28 Mbps.

After launch, the first groundstation to pick the S-band signal from JWST was the 10 m antenna from the Italian Space Agency in Malindi, Kenya. This groundstation commanded the telemetry rate to increase from 1 kbps to 4 kbps. After this, the spacecraft’s footprint continued moving to the east, and it was tracked for a few hours by the DSN in Canberra. One of the things that Canberra did was to increase the telemetry rate to 40 kbps, which apparently is the maximum to be used in the mission.

As JWST moved away from Earth, its footprint started moving west. After Canberra, the spacecraft was tracked by Madrid. Edgar Kaiser DF2MZ, Iban Cardona EB3FRN and other amateur observers in Europe received the S-band telemetry signal. When Iban started receiving the signal, it was again using 4 kbps, but some time after, Madrid switched it to 40 kbps.

At 00:50 UTC on December 26, the spacecraft made its first correction burn, which lasted an impressive 65 minutes. Edgar caught this maneouvre in the Doppler track.

Later on, between 7:30 and 11:30 UTC, I have been receiving the signal with one of the 6.1 metre dishes at Allen Telescope Array. The telemetry rate was 40 kbps and the spacecraft was presumably in lock with Goldstone, though it didn’t appear in DSN now. I will publish the recording in Zenodo as usual, but since the files are rather large I will probably reduce the sample rate, so publishing the files will take some time.

In the rest of this post I give a description of the telemetry of JWST and do a first look at the telemetry data.

## Waterfalls from the December 2021 eclipse frequency measurement

The HamSci Ham Radio Scienze Citizen Investigation community organized earlier this month the December 2021 Eclipse Festival of Frequency Measurement. The goal of this activity was to measure the frequency of HF time signals such as WWV and RWM over the course of ten days. The experiment lasted from December 1 to December 10, so it included the total eclipse over Antarctica of December 4, which happened between 5:29 and 9:37 UTC.

I participated in this activity with my HF station, which consists of a Hermes-Lite 2 beta2 DDC/DUC SDR transceiver and an end-fed random wire antenna about 17 metres long. I used a 10 MHz reference from a GPSDO as described in this post to lock the Hermes-Lite 2 sampling clock. Instead of measuring frequency in real time, I recorded IQ data at 200 sps for the WWV carrier at 5000, 10000 and 15000 kHz and for the RWM carrier at 4996, 9996 and 14996 kHz, so that the data could be post processed later with any kind of algorithms. I have published my recordings in the “December 2021 Eclipse Festival of Frequency Measurment IQ recording by station EA4GPZ” dataset in Zenodo.

In this post I process the IQ recordings to produce waterfalls that give us an overview of the data. The frequency measurement will be done in a later post.

## One month of Tianwen-1 remote sensing orbit

In a previous post, I described the remote sensing orbit into which Tianwen-1 had moved on November 8. Now it has been in this orbit for more than one month, and AMSAT-DL has been collecting telemetry almost daily with the 20 metre antenna at Bochum obseratory. Therefore, it is a good moment to review the state vector data and look at how the orbit has evolved with time.

Published
Categorised as Space

## Voyager 1 and Reed-Solomon

In one of my previous posts about Voyager 1, I stated that the Voyager probes used as forward error correction only the k=7, r=1/2 CCSDS convolutional code, and that Reed-Solomon wasn’t used. However, some days ago, Brett Gottula asked about this, citing several sources that stated that the Voyager probes used Reed-Solomon coding after their encounter with Saturn.

My source for stating that Reed-Solomon wasn’t used was some private communication with DSN operators. Since the XML files describing the configuration of the DSN receivers for Voyager 1 didn’t mention Reed-Solomon either, I had no reason to question this. However, the DSN only processes the spacecraft data up to some point (which usually includes all FEC decoding), and then passes the spacecraft frames to the mission project team without really looking at their contents. Therefore, it might be the case that it’s the project team the one who handles the Reed-Solomon code for the Voyagers. This would make sense specially if the code was something custom, rather than the CCSDS code (recall that Voyager predates the CCSDS standards). If this were true, the DSN wouldn’t really care if there is Reed-Solomon or not, and they might have just forgotten about it.

After looking at the frames I had decoded from Voyager 1 in more detail, I remarked that Brett might be right. Doing some more analysis, I have managed to check that in fact the Voyager 1 frames used Reed-Solomon as described in the references that Brett mentioned. In this post I give a detailed look at the Reed-Solomon code used by the Voyager probes, compare it with the CCSDS code, and show how to perform Reed-Solomon decoding in the frames I decoded in the last post. The middle section of this post is rather math heavy, so readers might want to skip it and go directly to the section where Reed-Solomon codewords in the Voyager 1 frames are decoded.

## Reed-Solomon bug in Queqiao

Queqiao is the communications relay satellite for the Chang’e 4 Chinese lunar lander mission to the far side of the Moon. It is in a halo orbit around the Earth-Moon Largrange L2 point and provides communications to the lander in Von Kármán crater.

Queqiao transmits telemetry in S-band, using the frequency 2234.5 MHz. The modulation and coding is similar to other recent Chinese probes, such as Chang’e 5 and Tianwen-1. Here I report an interesting bug that I found in the Reed-Solomon encoding performed by Queqiao.

## More data from Voyager 1

Back in September, I showed how to decode the telemetry signal from Voyager 1 using a recording made with the Green Bank Telescope in 2015 by the Breakthrough Listen project. The recording was only 22.57 seconds long, so it didn’t even contain a complete telemetry frame. To study the contents of the telemetry, more data would be needed. Often we can learn things about the structure of the telemetry frames by comparing several consecutive frames. Fields whose contents don’t change, counters, and other features become apparent.

Some time after writing that post, Steve Croft, from BSRC, pointed me to another set of recordings of Voyager 1 from 16 July 2020 (MJD 59046.8). They were also made by Breakthrough Listen with the Green Bank Telescope, but they are longer. This post is an analysis of this set of recordings.

## Computing the symbol error rate of m-FSK

How to compute the symbol error rate rate of an m-FSK modulation is something that comes up in a variety of situations, since the math is the same in any setting in which the symbols are orthogonal (so it also applies to some spread spectrum modulations). I guess this must appear somewhere in the literature, but I can never find this result when I need it, so I have decided to write this post explaining the math.

Here I show an approach that I first learned from Wei Mingchuan BG2BHC two years ago during the Longjiang-2 lunar orbiter mission. While writing our paper about the mission, we wanted to compute a closed expression for the BER of the LRTC modulation used in the uplink (which is related to $$m$$-FSK). Using a clever idea, Wei was able to find a formula that involved an integral of CDFs and PDFs of chi-squared distributions. Even though this wasn’t really a closed formula, evaluating the integral numerically was much faster than doing simulations, specially for high $$E_b/N_0$$.

Recently, I came again to the same idea independently. I was trying to compute the symbol error rate of $$m$$-FSK and even though I remembered that the problem about LRTC was related, I had forgotten about Wei’s formula and the trick used to obtain it. So I thought of something on my own. Later, digging through my emails I found the messages Wei and I exchanged about this and saw that I had arrived to the same idea and formula. Maybe the trick was in the back of my mind all the time.

Due to space constraints, the BER formula for LRTC and its mathematical derivation didn’t make it into the Longjiang-2 paper. Therefore, I include a small section below with the details.

Published
Categorised as Maths Tagged ,


text:
# Command-line script topic type¶

The script topic type provides a common documentation format for describing ad hoc scripts that are packaged with the LSST Stack. This topic type is oriented towards creating reference documentation; these topics are the canonical descriptions for a script’s command-line arguments, options, and functionality. Other topics, like how-to guides and tutorials, can link to these descriptions.

This script topic type works for any type of command-line executable (like shell scripts and compiled C++ executables) and relies on manually writing the usage, and documentation for options and arguments. If your script is written in Python and uses argparse, you can automate this reference documentation by using the argparse-based variant of the script topic type.

If the script is implemented in Python with an argparse-based command-line interface, refer to Argparse-based script topic type instead.

## Starter template¶

Create a new script topic from Slack.[1] Open a direct message with @sqrbot-jr and type:

create file

Then select Science Pipelines documentation > Script topic (generic).

 [1] The script topic file template is available in the lsst/templates repository.

For an example script named exampleScript.sh, the rendered template looks like this:

.. program:: exampleScript.sh

################
exampleScript.sh
################

.. Summary sentence that describes what the script does goes here.

.. code-block:: text

Usage: exampleScript.sh [OPTIONS]... [ARGS]

.. Positional arguments
.. ====================
..
.. .. option:: fixme
..
..    FIXME description of a positional argument.

Optional arguments
==================

.. option:: -h

Print the help message.

The next sections describe the key components of script topics.

## File name and location¶

The file must be named after the command-line executable, including any extension. For example, if the script is myScript.py, the topic’s file should be named myScript.py.rst.

The file must be located in the scripts/ subdirectory of the module documentation directory within a package.

For example, if the module’s namespace is lsst.example, the full path for the file is doc/lsst.example/scripts/myScript.py.rst.

## Preamble¶

The topic of the script topic file should have a program directive with the executable’s name as an argument:

.. program:: exampleScript.sh

This allows you to associate option directives further down the page with this executable in cross-references.

## Title¶

The title (top-level header) is the executable’s name (what you would type on the command line, assuming the executable is in the \$PATH), without any special formatting (like code literals).

## Summary sentence¶

Directly below the title, write a sentence that says what the script is for. Think of this sentence as a subtitle that helps a reader quickly understand what the script is for, without getting into too much detail.

## Description¶

After the summary sentence (a paragraph of its own), you can add additional paragraphs that discuss functionality in depth, and provide small examples of how the script might be used.

If necessary, organize these paragraphs into subsections.

## Usage¶

Before the options and arguments are documented, include a usage message inside a code-block directive.

The starter template includes a basic usage message. To learn more about formatting usage messages, see Wikipedia.

## Positional arguments (optional section)¶

The section named “Positional arguments” is where you document command-line arguments that are positional. Leave this section out if there aren’t any positional arguments.

Document each argument with an option directive. For example:

.. option:: file

Path of an input file.

## Optional arguments (optional section)¶

The section named “Optional arguments” is where you document options, like the -h option to produce a help message. Leave this section out if there aren’t any optional arguments.

Document each optional argument using the option directive, including the dash character (-):

.. option:: -h, --help

Print the help message and exit.

Notice how both the short and long forms of an option can be documented together. Of course, options don’t need to have both forms.

The option directive also works with options that have operands:

.. option:: --ref gitref

The Git commit SHA, tag, or branch name.

## Grouped argument sections (optional sections)¶

If the command-line interface has a large number of options, you might want to organize them into their own sections. This corresponds to how you would use the argparse.ArgumentParser.add_argument_group method in Python scripts.

Make sure the section name ends with the word “arguments” and start the section name with the name of the group. The content of this section is also made up of option directives.

Positional arguments
====================

.. option:: file

Path to the file

Optional arguments
==================

.. option:: -h, --help

Print the help message and exit.

.. option:: --verbose

Enable verbose logging.

XYZ arguments
=============

.. option:: --flag1 bar

Description of flag1.

.. option:: --flag2

Description of flag2.


text:
# What is the simplest radical form of 53?

Aug 26, 2016

Do you want to simplify $\sqrt{53}$ ?

#### Explanation:

What prime factors divide 53? 53 itself looks prime to me.

In order to simplify $53$ and then take the square root, you have to be able to factor 53 into smaller numbers, at least one of which is a perfect square.

For example, what is $\sqrt{144}$ ?
144 can be factored into 12 x 12 or ${12}^{2}$.
So you have $\sqrt{{12}^{2}}$ which is $12$ .

How about $\sqrt{20}$ ?
First, factor 20 as 5 x 4.
Then write 4 as ${2}^{2}$ .
You have $\sqrt{{2}^{2} \cdot 5}$, which equals $\sqrt{{2}^{2}} \cdot \sqrt{5}$, which equals $2 \sqrt{5}$.

I think that's what you want to do with $\sqrt{53}$, except you can't, because 53 can only be divided by itself and one - it's prime.

The simplest form of $\sqrt{53}$ is $\sqrt{53}$.

Here are the first 18 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, . . .


text:
# Emmanuel Caron (Centrale Nantes), 29 mars 2019

vendredi 29 mars 2019

Résumé : We consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator under general conditions on the design and on the error process. Whatever the design satisfying Hannan’s conditions, we define an estimator of the covariance matrix and we prove its consistency under very mild conditions. As an application, we show how to modify the usual tests on the linear model in this dependent context, in such a way that the type-I error rate remains asymptotically correct.


text:
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

# Math

Unless otherwise stated, the material in this guide is from The Learning Centre at Centennial College.  Content has been adapted for the NWP Learning Commons in March 2022. This work is licensed under a Creative Commons BY 4.0 International License.

Confidence Intervals

Confidence intervals are intervals that estimate a population parameter.

For example, it is very difficult to collect every data value to calculate the population mean $$\mu$$, or standard deviation $$\sigma$$. But, we can estimate the parameters using confidence .

 Confidence interval for a population mean with normal distribution: $$\sigma$$ is known: $\mu=\bar{x} \pm (z_{\alpha/2})\left( \frac{\sigma}{\sqrt{n}}\right)$ $$\sigma$$ is unknown: $\mu\approx \bar{x} \pm (z_{\alpha/2})\left( \frac{s}{\sqrt{n}}\right)$ where $$z_{\alpha/2}$$ is the z-value corresponding to an area $$\alpha/2$$ in the tail of a standard normal distribution.  Conditions Required: A random sample is selected from the target population. The distribution is approximately normal. The sample size $$n$$ is large (e.g., $$n\geq 30$$).

The confidence level is the probability that an interval estimator encloses the population parameter. For example, a 95% confidence level represents that there is a 95% chance that the confidence interval contains the population mean.

Common Misinterpretations:

It does not mean that there is a 95% chance that the population mean lies within the interval.

It also does not mean that the confidence interval contains 95% of the data values.

Commonly used confidence levels:

 Confidence Level $$100(1-\alpha)\%$$ $$\alpha$$ $$\alpha/2$$ $$z_{\alpha/2}$$ 90% 0.10 0.05 1.645 95% 0.05 0.025 1.960 99% 0.01 0.005 2.575

Example: A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a standard deviation equal to 6.4. Find a 95% and 99% confidence interval for $$\mu$$.

Solution:

Since the sample is large (n=100) and the distribution is normal, we can use the formula to calculate the confidence interval for the population mean using the z-table. The sample standard deviation is given (s=6.4).

95% confidence interval. $$z_{0.05/2}=1.960$$

\begin{align} \mu &\approx \bar{x} \pm (z_{0.05/2})\left( \frac{s}{\sqrt{n}}\right) \\ &\approx 83.2 \pm 1.960\left( \frac{6.4}{\sqrt{100}}\right) \\ &\approx 83.2 \pm 1.2544 \\ &\approx (81.9456,84.4544)\end{align}

There is a 95% chance that the interval (81.9456,84.4544) contains $$\mu$$.

99% confidence interval. $$z_{0.01/2}=2.575$$

\begin{align} \mu &\approx \bar{x} \pm (z_{0.01/2})\left( \frac{s}{\sqrt{n}}\right) \\ &\approx 83.2 \pm 2.575\left( \frac{6.4}{\sqrt{100}}\right) \\ &\approx 83.2 \pm 1.648 \\ &\approx (81.552,84.848)\end{align}

There is a 99% chance that the interval (81.552,84.848) contains $$\mu$$.

## Confidence Interval for Small Samples

For smaller distributions, the z-statistic is no longer an accurate measure because the small number of samples does not ensure that the distribution is normal. However, we can use the t-statistic to approximate a normal distribution.

 Confidence interval for small samples: If $$\sigma$$ is known, you can still use the z-statistic. If $$\sigma$$ is unknown, $\mu \approx \bar{x} \pm t_{\alpha/2}\left(\frac{s}{\sqrt{n}}\right)$ where $$t_{\alpha/2}$$ is the t-value corresponding to an area $$\alpha/2$$ in the upper tail of the Students' t-distribution based on $$(n-1)$$ degrees of freedom.

Conditions to use the t-statistic in a confidence interval:

• A random sample is selected from the target population.
• The population has a distribution that is approximately normal.
• $$\sigma$$ is not given.
• Sample size is small (e.g.,$$n < 30$$).

Example: Suppose you have selected a random sample of $$n=13$$ measurements from a distribution that is approximately normal. The sample reported $$\bar{x}=53.4g$$ and $$s=8.6g$$. Find the 98% confidence interval.

Solution:

Since the sample is small $$n=13$$ and $$\sigma$$ is not given, we will have to use the t-statistic.

98% confidence interval, degree of freedom = 12, $$\alpha=0.02/2=0.01$$, $$t_{0.01} = 2.681$$ from t-table

\begin{align} \mu &\approx \bar{x} \pm t_{0.02/2}\left(\frac{s}{\sqrt{n}}\right) \\ &\approx 53.4 \pm 2.681\left(\frac{8.6}{\sqrt{13}}\right) \\ &\approx 53.4 \pm 6.39475 \\ &\approx (47.00525,59.79475) \end{align}

There is a 98% chance that the interval (47.00525g,59.79475g) contains $$\mu$$.

## Confidence Interval for Population Proportion

Sometimes your data is expressed as a proportion or fraction of successes, $$\hat{p}$$, with proportional mean, $$p$$.

 Sampling Distribution of $$\hat{p}$$ The mean of the sampling distribution of $$\hat{p}$$ is $$p$$ The standard deviation of the sampling distribution of $$\hat{p}$$ is $$\sqrt{pq/n}$$; that is $$\sigma_{p}=\sqrt{pq/n}$$, where $$q=1-p$$  For large samples, the sampling distribution of $$\hat{p}$$ is approximately normal. A sample size is considered large if both $$n\hat{p}\geq15$$ and $$n\hat{q}\geq15$$
 Large-Sample Confidence Interval for p $p \approx \hat{p} \pm z_{\alpha/2}(\sigma_{\hat{p}}) = \hat{p} \pm z_{\alpha/2}\sqrt{\frac{pq}{n}} \approx \hat{p} \pm z_{\alpha/2}\sqrt{\frac{\hat{p}\hat{q}}{n}}$ where $$\hat{p}=\frac{x}{n}$$ and $$\hat{q}=1-\hat{p}$$

Conditions Required for a Valid Large-Sample Confidence Interval for p:

• A random sample is selected from the target population.
• The sample size n is large.

Example: A random sample of size $$n=196$$ yielded $$\hat{p}=0.64$$. Construct a 95% confidence interval for p.

Solution:

$$\hat{p}=0.64, \hat{q}=1-0.64=0.36, z_{0.05/2}=1.96$$

\begin{align} p &\approx \hat{p} \pm z_{\alpha/2}\sqrt{\frac{\hat{p}\hat{q}}{n}}\\ &\approx 0.64 \pm 1.96 \sqrt{\frac{(0.64)(0.36)}{196}} \\ &\approx 0.64 \pm 0.0672 \\ &\approx (0.5728,0.7072) \end{align}

There is a 95% chance the interval (0.5728,0.7072) contains p.


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# Is it possible to find a molecular formula from molar mass?

Aug 24, 2014

Mass spectroscopists have computer programs that use the precise masses of isotopes and their natural abundances to calculate all the possible combinations of C, H, O, N, etc. in a molecule and then match them to a given molar mass.

We mere mortals lack such tools. We need more information like an empirical formula to find a molecular formula from the molar mass.

Example

What is the molecular formula of a compound with a molar mass of 180.16 g/mol and an empirical formula of CH₂O?

Solution

Step 1. Find the molar mass of the empirical formula.

Molar mass = (12.01 + 2×1.008 + 16.00) g/mol = 30.016 g/mol

Step 2. Find the number of empirical formula units in the molecular formula.

No. of EF units in MF = "MF molar mass"/"EF molar mass" = (180.16"g/mol")/(30.016"g/mol") = 6.0021 ≈ 6

Step 3. Find the molecular formula.

Molecular formula = (CH₂O)₆ = C₆H₁₂O₆


text:
# Configuration

This section helps you to:

## Credentials

You need to obtain and properly configure your credentials so that the OLP CLI can connect to the HERE platform.

Your Credentials are used for authentication. The HERE platform uses the concept of apps and access key to control the access to resources. These are described in the Identity & Access Management Guide.

The credentials consist of the here.access.key.id and here.access.key.secret contained in a credentials.properties file. You can download this file from the platform portal when creating an access key for an app (see the procedure below in the Credentials Setup. The following snippet illustrates an example of a credentials.properties file:

here.user.id = HERE-01966c94-aaf1-4ae2-a1y6-6516b3f9b6c1
here.client.id = mzLcb1rL8nskvDQpCAAO
here.access.key.id = BELUTk45QdaYGgZ9A_IMTA
here.access.key.secret = 108lI7w9m8G_6sIw9kng-PXGoeHQQ-cv6xByNOuMcRYixZZp...
here.token.endpoint.url = https://account.api.here.com/oauth2/token

### Scopes

The HERE platform uses OAuth2 scopes as a mechanism to control access to certain resources. Each of the OLP CLI commands that support scope resolves the scope to use in the request in the following priority order:

1. --scope <project HRN>: An optional parameter that specifies the scope to use in the request.

2. here.token.scope: An optional attribute to include in the credentials used for the request.

3. Application default scope: If the client making the request has a default scope configured and neither of the above two parameters are present, the client's default scope will be used in the request.

4. If a scope is not found in either of the above three locations, the request will not use any scope.

### Profiles

Credentials profiles allow you to define multiple profiles to use different credentials for different projects. You can use credentials profiles to manage and organize multiple app credentials from multiple credentials.properties files.

Profiles and the related credentials are stored in the .here/olpcli.ini file in your home directory. You can manage profiles with the credentials commands. The .here/olpcli.ini file is created after you add your first profile with the olp credentials import command, as described in the Setup section below.

### Credentials Setup

1. In the platform portal, in the upper-right corner, click your account icon and select Apps & keys.
2. Click the Register new app button and specify the requested information.
3. In the Credentials tab, go to the OAuth 2.0 tab and click Create credentials.
4. In the dialog box that opens, click Download to download the credentials.properties file.

Once you click Close, you can no longer access your access key ID and access key secret.

5. To create a default profile and associate your credentials with it, run the following command:

 olp credentials import default credentials.properties

6. To verify that your credentials have been correctly configured, execute the command below in the directory that contains the OLP CLI JAR file:

 olp api token get

An output similar to the one below is generated if your credentials have been configured properly:

Token: eyJhbGciOiJSUzUxMiIsImN0eSI6IkpXVCIsImlzcyI6IkhFUkUiLCJhaWQiOiJtekxjYjFyTDhuc2t2RFFwQ0ZFRiIs
ImlhdCI6MTUyMTgwNjYyOCwiZXhwIjoxNTIxODkzMDI4LCJraWQiOiJqMSJ9.ZXlKaGJHY2lPaUprYVhJaUxDSmxibU1pT2lKQk
1qVTJRMEpETFVoVE5URXlJbjAuLmtGc0JMODJibEUxTHhCS1M3MEctcFEuZHhsb2psaklEQmdNVEdoMEFKMHAzUU9yeE9INXdhd
1hkWjVSLS1Kdkc3VFBoUkRWY3owcUFYZ0V2Y3kwOGpMdzBCR09sNjJfZ2pxeUNuLXhET3JtZV8xNUlkV0tJN2VxTUpZNTNJelRx
ZjhUSzdVVHlEUlJFVnBLRW5BN2FvR2MubFViMTNGYWdKMlVGZXVQZnZsVG44Y2JqTzdtbF9ncGpLamFUN0xmZFF0UQ.EPYB9Rdy
jCHFxrqpaEBWkPzhPmFrAPBKlkt8SQpcI0k71mH_vC6txh6Uv1NVQC4xYyWG7ueq5mb4mcQh1sCorcv15GwIH1R0v0NR_CRPh-M
DNSFtg8HNnWyC1ePsfUGpSqjucQW8RMdbsU03wDO50Pr3ctQI4BZrxiU4HW6tdQq9_TinizujACzE-LMZ6FlFAb6pPB8TDsFlY3
9OmBFXEanaPvZwE01dKjE1K_A_G1_TiJzWo4vwuNeD54HfmOf6hN1IE8-CCSKRoIFoIBiVNqqzyCybyovRlSCWzSaTNz4v9BD7N
2lDgEuBlpn3q0qTFppZzjEvzv3RicGrCC_tmB
Token Expires at: 2018-03-24T14:03:48.100Z

You can now use your credentials to connect to the HERE platform resources through the OLP CLI.

Keep your credentials private. Don't share them between workstations or users. Don't commit them to public repositories such as GitHub.

### Passing Credentials to the OLP CLI

The OLP CLI allows you to pass your credentials via optional parameters of the CLI commands or by setting environment variables. The OLP CLI resolves credentials in the following order:

1. --credentials <path to credentials file>: An optional parameter that you append to the end of an applicable CLI command. This parameter specifies the path to the credentials.properties file to use with the command.

For example, execute the command below:

olp catalog layer show hrn:here::data:::test-catalog test-layer --credentials credentials.properties

This shows the properties of the test-layer layer if your credentials allow you to access the hrn:here::data:::test-catalog catalog.

2. OLP_CREDENTIALS: An environment variable that defines the path to the credentials.properties file used for all CLI commands by default.

3. --profile <profile name>: An optional parameter that you append to the end of an applicable CLI command. This parameter specifies the name of the profile to use with the command.

For example, the following command shows a list of catalogs accessible to the olp-user profile, including all the public HERE platform catalogs:

 olp catalog list --profile olp-user

4. OLP_PROFILE: An environment variable that defines the name of the profile to use for all CLI commands by default.

5. default profile: A profile that you create by running the command below:

 olp credentials import default credentials.properties

6. credentials.properties default location: A path to the .here folder in your home directory where your credentials file is stored by default.

### Note

Some OLP CLI commands require that you specify a group ID. Your administrator must set up the relevant group IDs for your account and assign your application to the group. If your app is not assigned to a group, then the command produces an error. For more information on group IDs, see the Identity & Access Management Guide.

## Passing Parameters to the OLP CLI

The OLP CLI supports a set of characters that you can use to pass command parameters:

1. Space and equal (=) separators.

By default, command parameters are separated with spaces, but you can also use the equal (=) separator, as in the examples below:

 olp catalog list --profile <your_profile_name>

 olp catalog list --profile=<your_profile_name>

2. Tilde-prefix (~).

If you are using the tilde-prefix (~) to denote a user's home directory in Linux environments, you must use a space as tilde cannot be combined with the = separator:

 olp catalog layer stream put hrn:here:data:::catalog1 stream-layer1 --input ~/path/to/dir

3. Pipe (|) and dash (-) characters.

The pipe (|) character lets you take the output of one command and send it as input to another command. The dash (-) character allows capturing that output and passing it to a certain parameter of the other command.

In the example below, the catalog show command returns the configuration of the hrn:here:data:::catalog-1 catalog in JSON format. The catalog update command takes the hrn:here:data:::catalog-1 configuration (through --config -) to update the configuration of the hrn:here:data:::catalog-2 catalog, including catalog summary, name, description, and layer configuration:

 olp catalog show hrn:here:data:::catalog-1 --json | olp catalog update hrn:here:data:::catalog-2 --config -

## Output Format Options

The OLP CLI's default output is optimized for human readability. Such exit codes are used:

• 0: returned when a command succeeds.
• 1: returned when a command was executed with the invalid parameters.
• 2: returned when the invalid configuration files were used.
• 3: returned when a command fails.
• 4: returned when a command was executed on the non-existing resources (mostly catalogs).

All commands provide a --quiet flag that allows reducing the output to essential values only with no additional information.

Commands that display output in the console provide a --json flag. Depending on the command, this flag shows more additional information in the output in the JSON format. You can also parse JSON output with a script.

Alternatively, you can set the OLP_OUTPUT environment variable to json or quiet to choose the output format. However, the flags have a higher priority than the environment variable.

For example:

Linux
Windows
export OLP_OUTPUT=json
set OLP_OUTPUT=json

To disable a previously set output format, set OLP_OUTPUT to verbose, which is its default value.

## HTTP Proxy

You have two options for setting up a proxy in the OLP CLI configuration:

Linux
Windows
export HTTPS_PROXY=http://proxy.hostname.com:8000
set HTTPS_PROXY=http://proxy.hostname.com:8000

Use the same syntax for the ALL_PROXY variable.

You can also provide your proxy credentials using the following command:

Linux
Windows
export HTTPS_PROXY=http://username:password@proxy.hostname.com:8000
set HTTPS_PROXY=http://username:password@proxy.hostname.com:8000

### Proxy Settings Resolution Order

The OLP CLI resolves proxy settings in the following order:

1. OLP CLI proxy settings defined in the .here/olpcli.ini file in your home directory
2. HTTPS_PROXY environment variable
3. ALL_PROXY environment variable
4. Java proxy settings


text:
# Notation for continuous functions

Let's say $(X,\sigma)$ and $(X,\tau)$ are topological spaces, and $f$ is a continuous function from the former to the latter. (That is, the inverse images of elements of $\tau$ are elements of $\sigma$.) How would I write this? Saying:

Let $f:X\to X$ be continuous

clearly doesn't work, since they are meant to have separate topologies. However, saying:

Let $f:(X,\sigma)\to(X,\tau)$ be continuous

doesn't seem right, as the domain of $f$ is $X$, not the ordered pair $(X,\tau)$, and similarly for the codomain. Should I just do away with function notation completely, and say this?:

Let $f$ be a continuous function from the topological space $(X,\sigma)$ to the topological space $(X,\tau)$.

The same problem arises for metric spaces.

You can use the second form:

Let $f\colon (X,\sigma)\to(X,\tau)$ be continuous.

You're right that in the universe of sets, taken literally this notation implies that $f$ is one of the four functions from $\{\{X\}, \{X,\sigma\}\}$ to $\{\{X\}, \{X,\tau\}\}$ — hardly what you mean. The highlighted statement implicitly means that $f$ is a morphism in the category $\mathsf{Top}$ of topological spaces with morphisms all continuous functions. Anyone will understand you. Via the usual "forgetful functor" from $\mathsf{Top}$ to $\mathsf{Sets}$, the structure (the topologies) fall off, and $f$ is revealed to be just a function from $X$ to $X$.

Of course, you can use the third form too, but it's verbose.

The second and the third are both fine, and I consider them synomyms. It's quite common to "abuse notation" and say that the domain of the function is the whole structure instead of just the underlying set, if you're interested in structure preserving maps, like here. If the topologies are clear from context, they're often omitted, but here they should be mentioned explicitly as they have the same underlying set.

I would like to suggest an alternative:

Let $f:X \to X$ be $(\sigma,\tau)$-continuous.

This also works if topology is replaced by metrics or norms:

Let $f:X \to X$ be $(d_0,d_1)$-continuous.


text:
# Victoria Gitman

Victoria Gitman earned her Ph.D. under my supervision at the CUNY Graduate Center in June, 2007.  For her dissertation work, Victoria had chosen a very difficult problem, the 1962 question of Dana Scott to characterize the standard systems of models of Peano Arithmetic, a question in the field of models of arithmetic that had been open for over forty years. Victoria was able to make progress, now published in several papers, by using an inter-disciplinary approach, applying set-theoretic ideas—including a use of the proper forcing axiom PFA—to the problem in the area of models of arithmetic, where such methods hadn’t often yet arisen.  Ultimately, she showed under PFA that every arithmetically closed proper Scott set is the standard system of a model of PA.  This result extends the classical result to a large new family of Scott sets, providing for these sets an affirmative solution to Scott’s problem.  In other dissertation work, Victoria untangled the confusing mass of ideas surrounding various Ramsey-like large cardinal concepts, ultimately separating them into a beautiful hierarchy, a neighborhood of the vast large cardinal hierarchy intensely studied by set theorists.  (Please see the diagram in her dissertation.)  Victoria holds a tenure-track position at the New York City College of Technology of CUNY.

Victoria Gitman

Victoria Gitman, “Applications of the Proper Forcing Axiom to Models of Peano Arithmetic,”  Ph.D. dissertation for the Graduate Center of the City University of New York, June 2007.

Abstract. In Chapter 1, new results are presented on Scott’s Problem in the subject of models of Peano Arithmetic. Some forty years ago, Dana Scott showed that countable Scott sets are exactly the countable standard systems of models of PA, and two decades later, Knight and Nadel extended his result to Scott sets of size $\omega_1$. Here it is shown that assuming the Proper Forcing Axiom, every arithmetically closed proper Scott set is the standard system of a model of PA. In Chapter 2, new large cardinal axioms, based on Ramsey-like embedding properties, are introduced and placed within the large cardinal hierarchy. These notions generalize the seldom encountered embedding characterization of Ramsey cardinals. I also show how these large cardinals can be used to obtain indestructibility results for Ramsey cardinals.

# The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$

• J. D. Hamkins and T. A. Johnstone, “The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$,” Proc.~Amer.~Math.~Soc., vol. 137, iss. 5, pp. 1823-1833, 2009.
@ARTICLE{HamkinsJohnstone2009:PFA(aleph_2-preserving),
AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
TITLE = {The proper and semi-proper forcing axioms for forcing notions that preserve {$\aleph_2$} or {$\aleph_3$}},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {137},
YEAR = {2009},
NUMBER = {5},
PAGES = {1823--1833},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2470843 (2009k:03087)},
MRREVIEWER = {John Krueger},
DOI = {10.1090/S0002-9939-08-09727-X},
URL = {http://dx.doi.org/10.1090/S0002-9939-08-09727-X},
file = F
}

We prove that the PFA lottery preparation of a strongly unfoldable cardinal $\kappa$ under $\neg 0^\sharp$ forces $\text{PFA}(\aleph_2\text{-preserving})$, $\text{PFA}(\aleph_3\text{-preserving})$ and $\text{PFA}_{\aleph_2}$, with $2^\omega=\kappa=\aleph_2$.  The method adapts to semi-proper forcing, giving $\text{SPFA}(\aleph_2\text{-preserving})$, $\text{SPFA}(\aleph_3\text{-preserving})$ and $\text{SPFA}_{\aleph_2}$ from the same hypothesis. It follows by a result of Miyamoto that the existence of a strongly unfoldable cardinal is equiconsistent with the conjunction $\text{SPFA}(\aleph_2\text{-preserving})+\text{SPFA}(\aleph_3\text{-preserving})+\text{SPFA}_{\aleph_2}+2^\omega=\aleph_2$.  Since unfoldable cardinals are relatively weak as large cardinal notions, our summary conclusion is that in order to extract significant strength from PFA or SPFA, one must collapse $\aleph_3$ to $\aleph_1$.


text:
# Does $\int_{1}^{\infty} \frac{\mathrm dx}{x^{\alpha}-1}$ converge?

I did a quick search here but couldn't find a similar problem (it's probably out there somewhere...)
I'm stuck with this rather simple improper integral:

$\int_{1}^{\infty} \frac{1}{x^{\alpha}-1} \mathrm dx$

Now, I see that it could be divided into two seperate integrals, so as to tackle one "problem" at a time:

$\int_{1}^{\infty} \frac{1}{x^{\alpha}-1}dx=\int_{1}^{2}\frac{1}{x^{\alpha}-1}dx+\int_{2}^{\infty}\frac{1}{x^{\alpha}-1}dx$

The rightmost integral, $\int_{2}^{\infty}\frac{1}{x^{\alpha}-1}dx$, is convergent if and only if $\alpha>1$, that's easy to see.

My problem seems to be with the other one, from 1 to 2. I mean, I realize that if $\alpha\ge1$ it is divergent (I hope...). I can't seem to formally show that. It's possible to use the comparison test (well, for absolute convergence), but with what function?

This is probably very simple and I'm just having a "blank" moment. I'd appreciate any kind of help.

First it is easy to see that for $a \leq 1$, the integral diverges by comparing it with $\dfrac1{x-1}$.

For $a>1$, we can proceed as follows. Replace $x$ by $1/x$, we then get that $$\int_1^{\infty} \dfrac{dx}{x^a - 1} = \int_1^0 \dfrac1{1/x^a-1} \dfrac{-dx}{x^2} = \int_0^1 \dfrac{x^{a-2} dx}{1-x^a}$$ Let $f_n(x) = x^{a-2} \left(\displaystyle \sum_{k=0}^n x^{ak}\right) = \left(\displaystyle \sum_{k=0}^n x^{ak+a-2}\right)$. We have $$f(x) = \dfrac{x^{a-2}}{1-x^a} > f_n(x) \,\,\,\,\, \forall x \in (0,1)$$ Now $$\int_0^1 f_n(x)dx = \sum_{k=0}^n \dfrac1{ak+a-1} > \dfrac{H_{n+1}}{a}$$ Hence, we have that $$\int_0^1 f(x) dx > \dfrac{H_{n+1}}{a}$$ for all $n$. Hence, $$\int_1^{\infty} \dfrac{dx}{x^a - 1}$$ diverges for all $a\geq 0$

Hint: We only care about $\alpha\gt 0$, else there is bad trouble at $\infty$. Let $x=1+t$. We are interested in $(1+t)^\alpha-1$ for positive $t$ near $0$. Usin Taylor's Theorem, or otherwise, we have $(1+t)^\alpha-1=\alpha t+O(t^2)$. So if $t$ is positive and close enough to $0$, $(1+t)^\alpha -1\lt 2\alpha t$. Then use the Comparison Test to conclude that the integral diverges.

• I get it now. Thank you! – Guy Feb 7 '13 at 10:29
• @Guy After you ask a question here, if you get an acceptable answer, you should "accept" the answer by clicking the check mark ✓ next to it. This scores points for you and for the person who answered your question. You can find out more about accepting answers here: How do I accept an answer?, Why should we accept answers?. – Simply Beautiful Art Jul 18 '17 at 19:08

One might use the direct comparison test. If $a=0$, then the integrand is undefined everywhere.

Else, one might note that for $a>1$,

$$1<x<2\implies\frac1{x^a-1}>\underbrace{\frac1{a(x-1)}}_{\text{diverges}}+\frac1{2n}-\frac12\\\int_1^2\frac1{|a|(x-1)}~\mathrm dx=\infty$$

For $0<a<1$,

$$1<x<2\implies\frac1{x^a-1}>\frac1{x^{a+1}-1}\\(\text{see above for why it diverges})$$

For $a<0$, note that

$$x>2\implies\frac1{x^a-1}>\frac1{2^a-1}\\\int_2^\infty\frac1{2^a-1}~\mathrm dx=\infty$$


text:
# The best way to draw this branching diagram figure in an equation

What is the simple and the best way to draw this figure in an equation?

Thank you! (tikz is fine.)

(Hopefully, such that $\simeq$ sign in between PDIFF and PL is formulated nicely. My version I shared above the $\simeq$ sign is not very good looking.)

It is not up to me to decide what the "best" way is, but the following is simple IMHO.

\documentclass{article}
\usepackage{forest}
\begin{document}
\begin{forest}
[TOP
[PDIFF
[DIFF]
[PL,edge label={node [midway,above,sloped] {$\sim$} } ]
]
]
\end{forest}
\end{document}

• thank you +1, this is one of the best way"s" -- I did not know the "forest" \usepackage{forest} before! – wonderich Jun 28 '19 at 22:37
• @wonderich You're welcome. forest is IMHO one of the most amazing TikZ-based packages that I am aware of. – user121799 Jun 28 '19 at 22:40

Here another proposal using tikz-cd package:

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{newtxtext,newtxmath}
\usepackage{tikz-cd}
\tikzset{close/.style={outer sep=-7pt}}
\usepackage{graphicx}

\begin{document}
\begin{tikzcd}[column sep=0cm]
&\\
& \text{PDIFF} \arrow[ld, no head] \arrow[rd, close, "{\rotatebox{-40}{\scalebox{2.5}{$\sim$}}}", no head] & \\
\text{DIFF} &   & \text{PL}
\end{tikzcd}
\end{document}

• thank you +1, this is one of the best way"s" since I like tikzcd. :-) – wonderich Jun 29 '19 at 23:28
• @wonderich Welcome always for me :). I am happy to have help you. My regards. – Sebastiano Jun 30 '19 at 10:04

I draw by this simple way:

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\path (0,0) node (top) {TOP}
++(-90:1) node (pdiff) {PDIFF}
+(-130:1.5) node (diff) {DIFF}
+(-50:1.5) node (pl) {PL};

\draw (top)--(pdiff)--(diff)
(pdiff)--(pl) node[midway,sloped,above,yscale=.6]{$\sim$};
\end{tikzpicture}
\end{document}


text:
06-1350/Class Notes for Thursday September 14

The Mathematica notebook we wrote is here.

Jones Polynomial

The simplest way to define the Jones polynomial is via the Kauffman bracket. The idea is to eliminate all crossings using the rule:

In the right hand side, the first bracket is called the 0-smoothing and the second is called the 1-smoothing. To calculate the Kauffman bracket we must sum over all possible smoothings. For instance, for the trefoil, we 23 = 8 summands, one of which will be:

Each summand will have no crossing and thus will be a union of (possibly nested) unknots. We define the bracket polynomial of k unknots to be dk-1 for some indeterminate d. Our hopes that our polynomial in ℤ[d,A,B] will be an invariant under the Reidmeister moves. We first verify R2.

Collecting like terms and comparing we find AB = 1 and A2 + B2 + dAB = 0. Thus, we must have B = A-1 and d = -(A2 + A2). Things are looking bad, we still have two moves to verify and we already lost two of our variables.

We now verify R3. For this we remark that

The two diagrams with coefficients B coincide; and the diagrams with coefficients A differ by two R2 moves. Now we verify R1:

The right hand side evaluates to A + A-1(-A2 -A-2) = -A3 of the desired. This is unfortunate. One could salvage something by taking A to be one of the cube roots of -1; however, the right way out of this is to define another invariant which fails in the exactly the same way, and multiply it with the bracket polynomial.

Writhe

The invariant we are looking for is called the writhe. If D is a diagram of an oriented knot, we define

We choose +1 if the crossing is positive (the overpass goes over the underpass from left to right) and -1 if the crossing is negative (otherwise):

Lets have an example. Notice that the orientation of the knot is actually irrelevant.

We now show that the writhe is also invariant under R2 and R3, under R1 we gain ±1 depending which way we apply it. In R2, the two crossings have opposite signs; and in R3, the diagonal crossing doesn’t change sign and the other two are reversed.

It follows that 〈D〉⋅(-A-3)w(d) is a knot invariant. This is a polynomial in A, we now substitute q http://katlas.math.toronto.edu/drorbn/images/2/23/Mathtext2.png for A and call this the Jones polynomial (which strictly speaking, is not really a polynomial).


text:
# State whether each of the following diagrams define a function or not. Justify your answer.

## 1 Answer

Not a function.
answered Jun 29, 2014


text:
# I Field operators and the uncertainty principle

Tags:
1. Dec 23, 2017

### phoenix95

Hi,
I am reading QFT by Lancaster and Blundell. In chapter 4 of the book the field operators are introduced:
"Now, by making appropriate linear combinations of operators, specifically using Fourier sums, we can construct operators, called field operators, that create and annihilate particles, but this time they don’t create/annihilate particles in particular momentum states but instead they create/annihilate particles localized at particular spatial locations. Thus the operator defined by
ψ(x)=I/√ν Σp ape-ip.x"

Won't this violate the uncertainty principle? I thought maybe it just creates the particle, after which the particle obeys the relation, but in the very next example(4.1) they go ahead to find the position and momentum of the particle(which they do accurately it seems?). What am I missing here?

Thank you for your time

2. Dec 23, 2017

### Iliody

The exp(-ipx) means that it is a wave, it hasn't a sharp position.

3. Dec 24, 2017

### phoenix95

Oh so what does the operator mean then? Sum over all such waves with momentum p? What momentum state would that particle be in then?

EDIT: I thought Σe-ip.x was Fourier tranform, since even a bunch of coupled oscillators behave as uncoupled oscillators in Fourier space

Last edited: Dec 24, 2017
4. Dec 24, 2017

### Iliody

The operator $a^\dagger_{p,\lambda}$ is the square root of the light intensity, the amplitude (in the classical sense, not in the wavefunction sense) of the given mode. The exponential also is fourier, because the reason you ell. The operators $a^\dagger_{p,\lambda}$ and $a_{p,\lambda}$ satisfy the commutation relations of harmonic oscillator amplitude (in the classical sense, not in the wavefunction sense), called creation-annihilation operators. Also, ψ+(x)=I/√ν Σp ape-ip.x, but ψ(x)=I/√ν Σp ape-ip.x+I/√ν Σp apeip.x.

5. Dec 25, 2017

### vanhees71

Be careful with defining what's observable in relativistic QFT! E.g., I'd define "intensity" as in classical electrodynamics as the energy density of the em. field since it is (a) gauge invariant (nothing can be observed that is not gauge invariant) and (b) it is Lorentz covariant. The photon number isn't since there is no conserved current ti deine a Lorentz-invariant quantity of such a kind (indeed photons are strictly neutral). Usually the "number of photons" are defined as the total energy divided by a typical frequency. If there is no typical frequency, it's usually hard to define anything like a photon number that makes sense, but energy density always makes sense, no matter which photon state you are considering.

6. Dec 25, 2017

### Staff: Mentor

Why not the expectation value of the photon number operator? Of course most states are not eigenstates of this operator, and the expectation value in general won't be an integer, but that's no different from any other non-eigenstate in QM.

7. Dec 25, 2017

### vanhees71

The photon-number operator is not Lorentz invariant. What's measured are in fact invariant momentum distributions of photons,
$$E \frac{\mathrm{d} N}{\mathrm{d}^3 \vec{q}}.$$
Of course, the expectation value of any "number" (in relativistic physics defined via conserved currents like electric charge, net-baryon number etc.) needs not necessarily by integer valued although the observable itself can only take integer numbers. That's indeed no problem at all.

8. Dec 25, 2017

### Iliody

Maybe the photon number can be defined by an ideal detector in the next way: given the electromagnetic field mode that can excite the detector, given its energy levels of that mode, the photon number is the number of the energy levels below the energy level that the detector measure.

9. Jan 5, 2018

### Demystifier

It would be in a state with a completely undetermined momentum, in agreement with the uncertainty principle.

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text:
# How should I author decimal numbers?

We have to select a base language for authoring, to prevent multiple interpretations of the same input. AlgebraKiT’s base language for authoring is English.

That means that for authoring it is recommended to use the English notation for a.o. numbers (point notation as decimal separator) and domains (square vs round brackets) to make sure the student behavior is correct. In the interactive student exercise, AlgebraKiT uses the audience information to translate the authored exercise to the interactive version with the correct student behavior.

We do provide support to write numbers with decimal separator to some extent, but we can’t guarantee that this results in the desired behavior at all times.

##### Example

When authoring an algebra interaction with task $(3,4+2)$, AlgebraKiT needs to decide whether this is the value $5,4$ or whether this is the coordinate $(3, 6)$. Therefore, it is recommended to write numbers with the point separator, and coordinates with a space after the comma.

Note: in the Math Entry literal setting, you should author the input as you want the student to literally write the answer. In that situation you will always need to author the expression based on the audience.


text:
Thus, while repayment reduces the amount of money owed, this does not happen fast enough since the real value of the dollar now rises ('swelling of the dollar'). Money - Money - Monetary theory: The relation between money and what it will buy has always been a central issue of monetary theory. The quantity theory of money was initially known as the equation of exchanged. Keynes remarks that contrary to contemporaneous thinking, velocity and output were not stable but highly variable and as such, the quantity of money was of little importance in driving prices.[17]. {\displaystyle i} As a student, Fisher had shown particular talent and inclination for mathematics, but he found that economics offered greater scope for his ambition and social concerns. Q . ⋅ The Fisher Effect is an economic theory created by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates. After graduating from Yale, Fisher studied in Berlin and Paris. He was one of the founders of the Life Extension Institute, under whose auspices he co-authored the bestselling book How to Live: Rules for Healthful Living Based on Modern Science, published in 1915. The Cambridge economists also thought wealth would play a role, but wealth is often omitted for simplicity. In its modern form, the quantity theory builds upon the following definitional relationship. He argued... .mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 40px}.mw-parser-output .templatequote .templatequotecite{line-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0}. At least two Americans were prominent builders of the "temple," John Bates Clark and Irving Fisher. "[28] Irving Fisher stated on October 21 that the market was "only shaking out of the lunatic fringe" and went on to explain why he felt the prices still had not caught up with their real value and should go much higher. [19], Fisher was also an active social and health campaigner, as well as an advocate of vegetarianism, prohibition, and eugenics. teoria cuantitativa del dinero pdf reader. The basic identity underlying the quantity theory was first developed by Irving Fisher (1867–1947) in 1911. Once the Great Depression was in full force, he did warn that the ongoing drastic deflation was the cause of the disastrous cascading insolvencies then plaguing the American economy because deflation increased the real value of debts fixed in dollar terms. For the long-run, there has been stronger support for (1) and (2) and no systematic association of Far from velocity offsetting the movements of the quantity of money, it reinforces them. As financial intermediation grew in complexity and sophistication in the 1980s and 1990s, it became more so. quantity theory of money a theory that posits a direct relationship between the MONEY SUPPLY and the general PRICE LEVEL in an economy.. Friedman writes... What matters, said Keynes, is not the quantity of money. The resulting equation is known as the Fisher equation in his honor. , or There was a decided tendency on the part of these banks between 1900 and 1914 to bottle up gold when it flowed towards them and to part with it reluctantly when the tide was flowing the other way. (Snowden 2005 p. 483) Cambridge Equation Edit $Md=kPY$ k = desired currency holding = 1/Velocity Md = money demand Fisher Equation Edit $MV=PY$ $V$ = income velocity of the circulation of money 15–17. "The Debt-Deflation Theory of Great Depressions,". The Fisher effect describes the relationship between the inflation rate and the nominal interest rate. Khan Academy – Quantity theory of money – Part of a larger course on macroeconomics, this video describes the quantity theory of money and how parts of it are calculated. [13], Karl Marx modified it by arguing that the labor theory of value requires that prices, under equilibrium conditions, are determined by socially necessary labor time needed to produce the commodity and that quantity of money was a function of the quantity of commodities, the prices of commodities, and the velocity. David Hume (1748), "Of Interest," "Of Interest" in. When inflation is sufficiently low, the real interest rate can be approximated as the nominal interest rate minus the expected inflation rate. The Quantity Theory of Money from John Stuart Mill through Irving Fisher from the New School "Quantity theory of money" at Formularium.org – calculate M, V, P and Q with your own values to understand the equation How to Cure Inflation (from a Quantity Theory of Money perspective) from Aplia Econ Blog Scroll to chapter-preview, 1933a. Academic discussion remains over the degree to which different figures developed the theory. Q The relationship between money and prices has historically been associated with the quantity theory of money. [28] Still, practical identification of the relevant money supply, including measurement, was always somewhat controversial and difficult. It was Fisher who (following the pioneering work of Simon Newcomb) formulated the quantity theory of money in terms of the "equation of exchange:" Let M be the total stock of money, P the price level, T the amount of transactions carried out using money, and V the velocity of circulation of money, so that. [8] Fisher was also a pioneer of econometrics, including the development of index numbers. This portion of cash is commonly represented as k, a portion of nominal income ( It emphasized the distinction between real and nominal interest rates: where According to Fisher, “Other things remaining unchanged, as the quantity of money in circulation increases, the price level also increases in direct proportion and the value of money decreases and vice versa”. Milton Friedman (1987), "quantity theory of money". These theoretical considerations involved serious changes as to the scope of countercyclical economic policy. {\displaystyle P} Some concepts named after him include the Fisher equation, the Fisher hypothesis, the international Fisher effect, the Fisher separation theorem and Fisher market. [25] This theoretical advance is explained in Hirshleifer.[9]. Definition: Quantity theory of money states that money supply and price level in an economy are in direct proportion to one another. The resulting theory, one of considerable power and insight, was presented in detail in The Theory of Interest. Hazard. where, As an example, [31] As a proponent of Eugenics he helped found the Race Betterment Foundation in 1906. Will be grateful. , leaving 33 Institute of Economic Affairs. , Q might represent currency plus deposits in checking and savings accounts held by the public, The Cambridge version of the Quantity Theory of Money is now presented. ⋅ P ^ Irving Fisher (1911), The Purchasing Power of Money, ^ von Mises, Ludwig Heinrich; Theorie des Geldes und der Umlaufsmittel [The Theory of Money and Credit] ^ Capital Vol III, Chapter 34 ^ Milton Friedman (1956), “The Quantity Theory of Money: A Restatement” in Studies in the Quantity Theory of Money, edited by M. Friedman. Keynes argued that the price level was not strictly determined by the money supply. V This process will continue until the equality between the demand for and the supply of money is re-established. For example, a 10% increase in Nonetheless, Fisher's work was a very significant contribution and was immediately recognized and praised as first-rate by such European masters as Francis Edgeworth. It is distinct from a fee which the borrower may pay the lender or some third party. The Monetarist counter-position was that contrary to Keynes, velocity was not a passive function of the quantity of money but it can be an independent variable. 2 The Quantity Theory of Money Any exploration of the relationship between money and inflation almost necessarily begins with a discussion of the venerable “quantity theory of money” (QTM). In one empirical formulation, velocity was taken to be "the ratio of net national product in current prices to the money stock".[24]. Fisher espoused a more succinct explanation of the quantity theory of money, resting it almost exclusively on long run prices. .[27]. M [29] The transactions version of the quantity theory of money was provided by the American economist Irving Fisher in his book- The Purchasing Power of Money (1911). {\displaystyle P\cdot Q} This reflects availability … ⋅ [27], This theory was largely ignored in favor of Keynesian economics, in part because of the damage to Fisher's reputation caused by his public optimism about the stock market, just prior to the crash. The New Palgrave: A Dictionary of Economics, Archive for the History of Economic Thought, Herbert Scarf, William C.Brainard, "How to Compute Equilibrium Prices in 1891". It is the classical view of how money is used in the economy, and what variables it affects. [8] The quantity theory was developed by Simon Newcomb,[9] Alfred de Foville,[10] Irving Fisher,[11] and Ludwig von Mises[12] in the late 19th and early 20th century. unchanged. He famously predicted, nine days before the crash, that stock prices had "reached what looks like a permanently high plateau. [30], Fisher supported the legal prohibition of alcohol and wrote three booklets defending prohibition in the United States on grounds of public health and economic productivity. Also like Marx he believed that the theory was misrepresented. [29] But monetary aggregates remain a leading economic indicator. Empirical studies have found relations consistent with the models above and with causation running from money to prices. Q [26] Before the war (and indeed since) there was a considerable element of what was conventional and arbitrary in the reserve policy of the banks, but especially in the policy of the State Banks towards their gold reserves. Fisher is probably best remembered today in neoclassical economics for his theory of capital, investment, and interest rates, first exposited in his The Nature of Capital and Income (1906) and elaborated on in The Rate of Interest (1907). The quantity theory of money, sometimes called “The Fisherian Theory” simply states that a change in price can be related to a change in the money supply. His subsequent theory of debt deflation as an explanation of the Great Depression, as well as his advocacy of full-reserve banking and alternative currencies, were largely ignored in favor of the work of John Maynard Keynes. In actual experience, a change in n is liable to have a reaction both on k and k' and on r. It will be enough to give a few typical instances. [2] Joseph Schumpeter described him as "the greatest economist the United States has ever produced",[3] an assessment later repeated by James Tobin[4] and Milton Friedman.[5]. {\displaystyle P} Friedman described the empirical regularity of substantial changes in the quantity of money and in the level of prices as perhaps the most-evidenced economic phenomenon on record. M The Cambridge equation is thus: Assuming that the economy is at equilibrium ( Quote. 3. To mitigate this problem, some central banks, including the U.S. Federal Reserve, which had targeted the money supply, reverted to targeting interest rates. A week after he was admitted to Yale College his father died, at age 53. Fisher's debt-deflation scenario has since seen a revival since the 1980s. In the Cambridge approach, both the demand for and the supply of money are recognised as real determinants of the value of money. For example, if the amount of money in an economy doubles, QTM predicts that price levels will also double. Fisher's 1942 book with the concept behind the Unlimited Savings Accumulation Tax, a reform introduced in the United States Senate in 1995 by Senator Pete Domenici (R-New Mexico), former Senator Sam Nunn (D-Georgia), and Senator Bob Kerrey (D-Nebraska). d An application of the quantity-theory approach aimed at removing monetary policy as a source of macroeconomic instability was to target a constant, low growth fsiher of the money supply. and the price level {\displaystyle Y} Explaining Quantity Theory of Money. {\displaystyle P} [32], When his daughter Margaret was diagnosed with schizophrenia, Fisher had her treated at the New Jersey State Hospital at Trenton, whose director was the psychiatrist Henry Cotton. {\displaystyle M} M That is certainly true of monetarism which has benefited much from Keynes's work. and Wicksell's theory was considerably more complicated, beginning with interest rates in a system of changes in the real economy. The solution is to mint no more coinage until it recovers its par value. {\displaystyle Q} the corresponding price level, and Critics of the theory argue that money velocity is not stable and, in the short-run, prices are sticky, so the direct relationship between money supply and price level does not hold. He was one of the earliest American neoclassical economists, though his later work on debt deflation has been embraced by the post-Keynesian school. Fisher was a prolific writer, producing journalism as well as technical books and articles, and addressing various social issues surrounding the First World War, the prosperous 1920s and the depressed 1930s. ), Milton Friedman (1956), "The Quantity Theory of Money: A Restatement" in, Roy Green (1987), "real bills doctrine", in. In 1891, Fisher received the first Ph.D. in economics granted by Yale. Irving Fisher nonetheless remained convinced of the validity of Cotton's treatment.[33]. What matters is the part of total spending which is independent of current income, what has come to be called autonomous spending and to be identified in practice largely with investment by business and expenditures by government. {\displaystyle M} That experience sparked in him a vocation as a health campaigner. Keynes had originally been a proponent of the theory, but he presented an alternative in the General Theory. A reduction in output, in trade and in employment. The "equation of exchange" relating the supply of money to the value of money transactions was stated by John Stuart Mill[7] who expanded on the ideas of David Hume. Friedman (1987), "quantity theory of money", p. 19. In the 1890s, according to Joseph A. Schumpeter there emerged {\displaystyle P\cdot Q} in (1) but with much variation in the precision, timing, and size of the relation. February, Learn how and when to remove these template messages, Learn how and when to remove this template message, An Enquiry into the Nature and Effects of the Paper Credit of Great Britain, The General Theory of Employment, Interest and Money, Capital Vol I, Chapter 3, B. "Irving Fisher on the International Transmission of Booms and Depressions through Monetary Standards. As restated by Milton Friedman, the quantity theory emphasizes the following relationship of the nominal value of expenditures [14] Marx did not reject the basic concept of the Quantity Theory of Money, but rejected the notion that each of the four elements were equal, and instead argued that the quantity of commodities and the price of commodities are the determinative elements and that the volume of money follows from them. The theory above is based on the following hypotheses: An application of the quantity-theory approach aimed at removing monetary policy as a source of macroeconomic instability was to target a constant, low growth rate of the money supply. He concluded that economic agents (individuals, firms, governments) want to hold a certain quantity of real, as opposed to nominal, money balances. Once again, these were not counterfeits but imitations.
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text:
Partitioning Sparse Rectangular Matrices for Parallel Processing

Abstract

We are interested in partitioning sparse rectangular matrices for parallel processing. The partitioning problem has been well-studied in the square symmetric case, but the rectangular problem has received very little attention. We will formalize the rectangular matrix partitioning problem and discuss several methods for solving it. We will extend the spectral partitioning method for symmetric matrices to the rectangular case and compare this method to three new methods — the alternating partitioning method and two hybrid methods. The hybrid methods will be shown to be best.

Publication
In Solving Irregularly Structured Problems in Parallel
Date
Citation
T. G. Kolda. Partitioning Sparse Rectangular Matrices for Parallel Processing. In Solving Irregularly Structured Problems in Parallel, 5th International Symposium, IRREGULAR’98, Berkeley, CA (1998-08-09 to 1998-08-11), A. Ferreira and others (eds.), Lecture Notes in Computer Science, Vol. 1457, No. 1457, Springer Berlin Heidelberg, pp. 68-79, 1998. https://doi.org/10.1007/BFb0018528

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BibTeX

@inproceedings{Ko98,
author = {Tamara G. Kolda},
title = {Partitioning Sparse Rectangular Matrices for Parallel Processing},
booktitle = {Solving Irregularly Structured Problems in Parallel},
eventtitle = {5th International Symposium, IRREGULAR'98},
venue = {Berkeley, CA},
eventdate = {1998-08-09/1998-08-11},
editor = {A. Ferreira and others},
series = {Lecture Notes in Computer Science},
volume = {1457},
number = {1457},
publisher = {Springer Berlin Heidelberg},
pages = {68-79},
year = {1998},
doi = {10.1007/BFb0018528},
}