text:
# SCCP-1: SCCP Purpose and Guidelines

Author Kain Warwick Implemented Governance Ethereum & Optimism TBD TBD 2019-06-17

## What is an SCCP?

SCCP stands for Synthetix Configuration Change Proposal. SCCP's are documents to make a case for modifying one of the system configuration variables. The intent is to provide a clear and detailed history behind each configuration change and the rationale behind it at the time it was implemented. The author of the document is responsible for building consensus within the community and documenting dissenting opinions.

## SCCP Rationale

We intend SCCPs to be the primary mechanisms for proposing configuration changes to Synthetix. Because they are maintained as text files in a versioned repository, their revision history is the historical record of the configuration change proposal.

It is highly recommended that a single SCCP contain a single variable change. The more focused the SCCP, the more successful it is likely to be.

An SCCP must meet certain minimum criteria. It must be a clear and complete description of the proposed variable change.

## SCCP Work Flow

Parties involved in the process are the author, the SIP editors, and the Synthetix Engineering Team.

Before you begin, vet your idea, this will save you time. Ask the Synthetix community first if the proposed change is original to avoid wasting time on something that will be rejected based on prior research (searching the Internet does not always do the trick). It also helps to make sure the idea is applicable to the entire community and not just the author. Just because an idea sounds good to the author does not mean it will have the intend effect. The appropriate public forum to gauge interest around your SCCP is the Synthetix Discord.

Your role as the champion is to write the SCCP using the style and format described below, shepherd the discussions in the appropriate forums, and build community consensus around the idea. Following is the process that a successful SCCP will move along:

[ WIP ] -> [ PROPOSED ] -> [ APPROVED ] -> [ IMPLEMENTED ]

Each status change is requested by the SCCP author and reviewed by the SIP editors. Use a pull request to update the status. Please include a link to where people should continue discussing your SCCP. The SIP editors will process these requests as per the conditions below.

• Work in progress (WIP) -- Once the champion has asked the Synthetix community whether an idea has any chance of support, they will write a draft SCCP as a pull request.

• Proposed If agreeable, SIP editor will assign the SCCP a number (generally the issue or PR number related to the SCCP) and merge your pull request. The SIP editor will not unreasonably deny an SCCP. Proposed SCCPs will be discussed on governance calls and in Discord. If there is a reasonable level of consensus around the change on the governance call the change will be moved to approved. If the change is contentious a vote of token holders may be held to resolve the issue or approval may be delayed until consensus is reached.

• Approved -- This SCCP has passed community governance and is now being prioritised.

• Implemented -- This SCCP has been implemented and the variable changed on mainnet.

## What belongs in a successful SCCP?

Each SCCP should have the following parts:

• Preamble - RFC 822 style headers containing metadata about the SCCP, including the SCCP number, a short descriptive title (limited to a maximum of 44 characters), and the author details.
• Simple Summary - “If you can’t explain it simply, you don’t understand it well enough.” Provide a simplified and layman-accessible explanation of the SCCP.
• Abstract - a short (~200 word) description of the variable change proposed.
• Motivation (*optional) - The motivation is critical for SCCPs that want to update variables within Synthetix. It should clearly explain why the existing variable is not incentive aligned. SCCP submissions without sufficient motivation may be rejected outright.
• Copyright Waiver - All SCCPs must be in the public domain. See the bottom of this SCCP for an example copyright waiver.

## SCCP Formats and Templates

SCCPs should be written in markdown format. Image files should be included in a subdirectory of the assets folder for that SCCP as follows: assets/sccp-X (for sccp X). When linking to an image in the SCCP, use relative links such as ../assets/sccp-X/image.png.

Each SCCP must begin with an RFC 822 style header preamble, preceded and followed by three hyphens (---). This header is also termed "front matter" by Jekyll. The headers must appear in the following order. Headers marked with "*" are optional and are described below. All other headers are required.

 sip: (this is determined by the SIP editor)

 title:

 author: <a list of the author's or authors' name(s) and/or username(s), or name(s) and email(s). Details are below.>

 * discussions-to: <a url pointing to the official discussion thread>

 status: < WIP | PROPOSED | APPROVED | IMPLEMENTED >

 created:

 * updated:

 * requires: <SIP number(s)>

Headers that permit lists must separate elements with commas.

Headers requiring dates will always do so in the format of ISO 8601 (yyyy-mm-dd).

#### author header

The author header optionally lists the names, email addresses or usernames of the authors/owners of the SCCP. Those who prefer anonymity may use a username only, or a first name and a username. The format of the author header value must be:

or

Random J. User

if the email address is not given.

#### discussions-to header

While an SCCP is in WIP or Proposed status, a discussions-to header will indicate the mailing list or URL where the SCCP is being discussed.

#### created header

The created header records the date that the SCCP was assigned a number. Both headers should be in yyyy-mm-dd format, e.g. 2001-08-14.

#### updated header

The updated header records the date(s) when the SCCP was updated with "substantial" changes. This header is only valid for SCCPs of Draft and Active status.

#### requires header

SCCPs may have a requires header, indicating the SCCP numbers that this SCCP depends on.

## Auxiliary Files

SCCPs may include auxiliary files such as diagrams. Such files must be named SCCP-XXXX-Y.ext, where “XXXX” is the SCCP number, “Y” is a serial number (starting at 1), and “ext” is replaced by the actual file extension (e.g. “png”).

## SIP Editors

The current SIP editors can be found listed in SIP-1

## SIP Editor Responsibilities

For each new SCCP that comes in, an editor does the following:

• Read the SCCP to check if it is ready: sound and complete. The ideas must make technical sense, even if they don't seem likely to get to final status.
• The title should accurately describe the content.
• Check the SCCP for language (spelling, grammar, sentence structure, etc.), markup (Github flavored Markdown), code style

If the SCCP isn't ready, the editor will send it back to the author for revision, with specific instructions.

Once the SCCP is ready for the repository, the SIP editor will:

• Assign an SCCP number (generally the PR number or, if preferred by the author, the Issue # if there was discussion in the Issues section of this repository about this SCCP)

• Merge the corresponding pull request

• Send a message back to the SCCP author with the next step.

Many SCCPs are written and maintained by developers with write access to the Ethereum codebase. The SIP editors monitor SCCP changes, and correct any structure, grammar, spelling, or markup mistakes we see.

The editors don't pass judgment on SCCPs. We merely do the administrative & editorial part.

## History

The SCCP document was derived heavily from the EIP Ethereum Improvement Proposal document in many places text was simply copied and modified. Any comments about the SCCP document should be directed to the SIP editors. The history of the EIP is quoted below from the EIP document for context:

• "This document (EIP) was derived heavily from Bitcoin's BIP-0001 written by Amir Taaki which in turn was derived from Python's PEP-0001. In many places text was simply copied and modified. Although the PEP-0001 text was written by Barry Warsaw, Jeremy Hylton, and David Goodger, they are not responsible for its use..." *

June 10, 2019: SCCP-1 has been drafted and submitted as a PR.

See the revision history for further details, which is also available by clicking on the History button in the top right of the SCCP.

### Bibliography

Copyright and related rights waived via CC0.


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## CryptoDB

### Paper: Perfect Hash Families with Few Functions

Authors: Simon R. Blackburn URL: http://eprint.iacr.org/2003/017 Search ePrint Search Google An {\em $(s;n,q,t)$-perfect hash family} is a set of functions $\phi_1,\phi_2,\ldots ,\phi_s$ from a set $V$ of cardinality $n$ to a set $F$ of cardinality $q$ with the property that every $t$-subset of $V$ is injectively mapped into $F$ by at least one of the functions $\phi_i$. The paper shows that the maximum value $n_{s,t}(q)$ that $n$ can take for fixed $s$ and $t$ has a leading term that is linear in $q$ if and only if $t>s$. Moreover, for any $s$ and $t$ such that $t>s$, the paper shows how to calculate the coefficient of this linear leading term; this coefficient is explicitly calculated in some cases. As part of this process, new classes of good perfect hash families are constructed.
##### BibTeX
@misc{eprint-2003-11735,
title={Perfect Hash Families with Few Functions},
booktitle={IACR Eprint archive},
keywords={combinatorial cryptography},
url={http://eprint.iacr.org/2003/017},
note={ s.blackburn@rhul.ac.uk 12080 received 28 Jan 2003},
author={Simon R. Blackburn},
year=2003
}

format: plain


text:
Flux of a vector and parametric equation

Homework Statement

Compute the flux of a vector field ##\vec{v}## through the unit sphere, where

$$\vec{v} = 3xy i + x z^2 j + y^3 k$$

Homework Equations

Gauss Law:
$$\int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$

The Attempt at a Solution

Ok so after applying Gauss Law, one gets
$$\int 3y dV$$
and after converting it into a spherical integral I get
$$3 \int_0^{ \pi} \sin^2 \theta d \theta \int_0^{2 \pi} \sin \phi d \phi = 0$$ since integral of sin over a full period is. Is this correct? or if not, where did I go wrong?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
2021 Award
It looks fine, but you do not need to actually do the spherical parametrisation. You could just use that the integrand is asymmetric over a symmetric region so the result must be zero.

Edit: Also, you are missing the radial part of the integral, but it will not matter.

Xsnac and alejandromeira
Xsnac I've been making the transformation right now and seems me that your work is ok.

Xsnac
It looks fine, but you do not need to actually do the spherical parametrisation. You could just use that the integrand is asymmetric over a symmetric region so the result must be zero.

Edit: Also, you are missing the radial part of the integral, but it will not matter.
Thanks. Regarding the radial part, it specified it's unit sphere therefore constant, and = 1 so I neglected it.

It looks fine, but you do not need to actually do the spherical parametrisation. You could just use that the integrand is asymmetric over a symmetric region so the result must be zero.

Edit: Also, you are missing the radial part of the integral, but it will not matter.
Yes, visualizing the field in the space there are a symetry in the plane XZ, then like the volume has also spherical symetry around the point (0,0,0) we don't need to calculate anything. So is more fun!!!

Last edited:
Orodruin
Staff Emeritus


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# Log-scale with concentrated data using integers

I have a data set with a range of 0 to 65,000. The vast majority of data points (it is a huge sample) are concentrated between 0 and 1000. There is only one point that has 65,000. I want to plot this using a semi-logarithmic plot. However, I would like the graph to have around 50 points. If I use scales like 2,4,6,8,16,32,64,128,256 etc I have only a couple of points. But If I use a multiple of 1.1 or 1.5 etc, the scales are not integers. Is there a standard way to ensure you more concentrated intervals at a lower level on the scale?

Cheers,

s

> x <- unique(round(1.25^(0:50)))


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# Showing two equations are identical.

• Feb 7th 2011, 04:22 PM
mandy9008
Showing two equations are identical.
X(t)=1/(√2) (cos(ωt))
Y(t)=cos(ωt+φ)

Demonstrate using trigonometry and algebra that the two equations are identical.
• Feb 7th 2011, 04:25 PM
Ackbeet
Those two equations are not identical. The amplitude of X is 1/(√2), whereas the amplitude of Y is 1. There's no way those two equations are identical. Is this part of a larger problem? If so, please state the original problem, word-for-word.
• Feb 7th 2011, 04:38 PM
mandy9008
Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.

Demonstrate using trigonometry and algebra that the two equations are identical.
• Feb 7th 2011, 05:52 PM
TheEmptySet
Quote:

Originally Posted by mandy9008
Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.

What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.

Demonstrate using trigonometry and algebra that the two equations are identical.

Attachment 20710

As Ackbeet said they cannot be equal as the have different amplitudes!. Here is an animated plot.

http://www.mathhelpforum.com/math-he...2&d=1297133353

In the above plot $\varphi$ goes from $-2\pi < \varphi < 2\pi$


text:
An Easy Way to Make Money on Bug Bounty

Surely you've heard the expression «bug hunting» many times. I dare to assume, you won't mind earning one or two hundred (or even thousand) dollars by finding a potential vulnerability in someone's program. In this article, I'll tell you about a trick that will help analyzing open source projects in order to find such vulnerabilities.

Bug Bounties on Free and Open Source Software — what is it?

Bug Bounty is a common name for various programs, where website and software developers offer cash rewards for finding bugs and vulnerabilities. In addition to well-known Bug Bounty programs from such large corporations, as Apple or Microsoft, there are also programs for searching vulnerabilities in open source projects.

Many of them can be found on HackerOne, but perhaps the largest is FOSSA — Free and Open Source Software Audit. It's a program on searching vulnerabilities in various open source projects, sponsored by the European Union. The total prize fund is an impressive sum — as much as 850,000 euros!

How to take part?

First, you need to register on HackerOne. We'll need only open source projects. There is a whole list on HackerOne.

If you'd like to take part in Bug Bounty from the European Union, the list of projects, participating in this program, can be found here. For most projects, it will be enough to be registered on HackerOne, but many of listed programs are also on the intigriti.com website.

To participate, you have to choose an appropriate project for yourself and then carefully read the terms of participation. If you agree with them, go to a practical part.

To find a vulnerability and get your money, you'll just need to download a project (or clone it from GitHub) and thoughtfully analyze each code line, examining each expression for potential errors. If you find something, that can affect program security — make a report and send to developers. If they rate your finding as worthy to be rewarded — you have your money in your pocket :).

But where is the simplicity?

The simple part is that you don't have to analyze the code only manually. There are tools that let you search for errors in code automatically. For example — static code analyzers. I prefer using our tool — PVS-Studio. PVS-Studio analyzer is able to find errors in code, written in C++, C# and Java, as well as has a user-friendly interface. In addition, there are several options of its free usage. Anyway, there are other various code analyzers.

Of course, static analyzers can reveal not all errors. Never mind! After all, we have a purpose to find errors quickly and easily, and not to find them all.

Once the project is downloaded and built, it will take only a couple of clicks to start the analysis. The result will be a report with some (usually considerable) number of warnings generated by the analyzer. In PVS-Studio, they are classified into three levels of certainty. You should start with the first level of warnings, so the orange and yellow levels can be weeded out from the analysis result.

An example of filtering the results of the analysis.

Thus, you'll only need to look though the rest warnings and choose the places that may pose the greatest danger. It is worth checking whether it is possible to reproduce any of them directly when running the program. If you manage to do it — it will not only increase the chances that developers will accept the report, but also certainly increase the amount of payment. In this case, visibility is your best friend.

It's also worth considering whether the bug you found affects the security of the program. After all, in this case, the amount paid to you will be several times more :)

The screenshot shows the Visual Studio interface. However, don't let it mislead you. The analyzer can be used not only as a plugin for Visual Studio, but also on its own, including the Linux and macOS environments.

Pros of this Approach

First, using a static analyzer is one of the easiest ways to find bugs. You don't have to have any special knowledge to use code analyzers: you just need to understand the language in which the code is written.

Secondly, analyzers are attentive. They don't get tired and don't lose their vigilance, unlike a human being. Therefore, they can be used to analyze as large code bases as you like with almost minimal cost.

Third, analyzers often have more knowledge than humans. What does it mean? Let me explain my thoughts with the example from the Android kernel code:

static void FwdLockGlue_InitializeRoundKeys() {
unsigned char keyEncryptionKey[KEY_SIZE];
....
memset(keyEncryptionKey, 0, KEY_SIZE); // Zero out key data.
}

It would seem, where's an error here?

It turns out, that a compiler, seeing that an array isn't used anywhere else, can optimize the code and remove the call of the memset function from it. And it'll do it only when building the release configuration. Everything would be fine, but only the encription key will remain in the RAM uncleared for some time, this way it can be obtained by an intruder. A real security breach!

In addition, it can be hardly found by yourself: in the debugging mode the call of memset works fine. Tests also won't be of help… The only thing that remains is to be aware and remember about this feature yourself.

Finally, the fourth point. One of the most useful advantages of using static analysis when chasing for Bug Bounty is speed. It's true that you can check two, three, four project in one evening — but that's not all.

The main thing is that you can be the first. While the award is offered for finding bugs in any project, the project continues to be refined and developed. Developers ship new releases and new features along with new code and new space for errors. When using the approach I've described, you'll be able to targetedly consider new errors and potential vulnerabilities in the very first day they're released.

Potential Vulnerabilities

An attentive reader may be puzzled:

Wait, wait! On the one hand, you're saying about searching for errors in code in programs, on the other hand — you're mentioning potential vulnerabilities. Vulnerabilities are more interesting in terms of Bug Bounty. Please, clarify what you mean!

The fact of the matter is that errors and potential vulnerabilities are basically the same thing. Sure, only a few errors/potential vulnerabilities prove to be real vulnerabilities in further research. However, a harmless blunder and crucial vulnerability might look exactly the same in code. The article "How Can PVS-Studio Help in the Detection of Vulnerabilities?" gives several seemingly common bugs that are now known to be vulnerabilities.

By the way, according to the report by National Institute of Standards and Technology (NIST), about 64% of vulnerabilities in applications relate to software errors, not issues directly related to security.

So grasp the nettle, get PVS-Studio and start searching for errors and safety flaws! Classification according to the CWE will be of great help here.

Conclusion

Hopefully, I helped a reader in his searching for that very bugs that will bring him honoring and monetary reward. I'm sure that static analysis will help in this! Remember that developers usually don't have time to analyze bugs in detail, so you'll have to prove that your finding can actually affect the program. The best way is to visually reproduce it. And remember: the more the bug destructs security — the more you'll get paid for it.

Well, that's it. Good luck in searching for a reward!
PVS-Studio
Static Code Analysis for C, C++, C# and Java


text:
# Just how do I mount an ISO?

I was wanting to recognize if Ubuntu features a typical means of placing ISOs. I checked out online and also located a number of manuscripts that can do it.

This to me feels like core capability, is it supplied by default in Ubuntu. Otherwise where is the most effective and also most basic mounter for ISOs.

0
2019-05-05 16:31:33
Source Share

A choice for promptly ordering documents off of an iso to DreadPirateJeff is remedy of loopback placing isos is the bsdtar(1) package.

sudo apt-get install bsdtar

For instance, to order the details construct details off of the Ubuntu 10.10 i386 livecd, which is had in the/. disk/info documents on the iso and also unload it to STDOUT, you would certainly do

bsdtar -x -O -f ubuntu-10.10-desktop-i386.iso .disk/info

which would certainly return

Ubuntu 10.10 "Maverick Meerkat" - Release i386 (20101007)

Given that it is an alternative tar energy, you can certainly extract numerous documents to disk. The benefit is that you can do all the above without origin advantages, unlike loopback places.

(Another choice is the isoinfo(1) energy from the genisoimage package ; nonetheless, it is a little much less uncomplicated to make use of than bsdtar.)

0
2019-05-31 22:51:34
Source

I assume the most convenient device for placing ISOs is AcetoneISO, it is really comparable to DaemonTools for Windows. Offer it a shot

0
2019-05-31 01:29:33
Source

Brasero which features Ubuntu has the ability to create and also open (to adjust) ISOs. If you're seeking a means to mount an ISO so it's materials are readily available like a "drive" you might intend to make use of merely Right Click the ISO and also pick "Open With Archive Mounter" which will certainly mount the ISO as a drive and also you need to see it detailed under the Places food selection.

This all thinks you are making use of 10.04

0
2019-05-08 09:24:03
Source

I constantly made use of Gmount - iso to mount ISO documents.

apt-get install -y gmountiso

0
2019-05-08 09:21:19
Source

A choice to archive - mounter is Furius ISO Mount which not just places ISOs yet can

• examine checksums,
• create checksums
• call nautilus for documents surfing
• call brassero to melt to CD.

apt :furiusisomount

0
2019-05-08 09:20:24
Source

If you favor to maintain it old-fashioned, in an incurable :

sudo mount /path/to/iso /path/to/mountpoint -o loop

This, certainly, will certainly not permit you to modify the ISO as the various other stated devices will, yet if you simply require to promptly get involved in one and also draw a couple of documents from it, functions like a beauty : -)

0
2019-05-08 08:09:56
Source


text:
# Category Archives: combinatorial optimization

## Python throw-back: making mazes again

I had an escapist hobby that is captured in the history of this blog, making maze [link], and I need escape again. And now I have a 5-year-old User for the output! Cool things: the maze-making code from 7 years ago was pretty easy to get working again [links, links]; the scientific python ecosystem now has notebooks! [link]

[Photo of done mazes on paper.]

Comments Off on Python throw-back: making mazes again

Filed under combinatorial optimization

## Old Maze Making Code

Playing around with that GIS optimization stuff was a chance for me to revisit some maze-making code I wrote a few years ago: https://healthyalgorithms.com/2011/01/07/piggies-and-mazes/ I wonder what age kids it will be good for.

Comments Off on Old Maze Making Code

Filed under combinatorial optimization

## Movie about a healthy algorithm for matching kidney transplants

This is a fun movie. Nice motion graphics, and camera work. The sound design is good too, although I found the jazz in the background distracting. And I love this research area. I think some colleagues at CMU were starting to work on it right when I was leaving grad school. I’ll share it on healthy algorithms went I have some time to post things.

–Abie

From: Sommer Gentry
Sent: Monday, November 11, 2013 12:25 PM
To: abie
Subject: a movie link for Healthy Algorithms?

Dear Abraham,

I hope this email finds you well. I am enjoying your blog!

I am writing to let you know about a short documentary that features me and my husband and a nice mathematical modeling problem for helping people get kidney transplants. Its moving principle is to sell operations research to a lay audience by explaining the kidney exchange problem in great detail. It has some nice animations that describe the steps of modeling and solving an integer program, at a level for absolute beginners.

Maybe you’d find it interesting enough to put on your blog. In any case, thanks for checking it out.

best,
Sommer

Comments Off on Movie about a healthy algorithm for matching kidney transplants

Filed under combinatorial optimization

## Power of SPARQL?

Is a SPARQL query computationally powerful enough to test (s,t)-connectivity? I don’t think so, but I don’t understand the mysterious PropertyPath, and even without it, I’m not sure. Tell me on Stack Overflow.

1 Comment

Filed under combinatorial optimization

## A simple optimization problem I don’t know how to solve (from DCP)

Inspired by the recent 8F workshop, I’m trying to write up theory challenges arising from global health. And I’m trying to do it with less background research, because avoiding foolishness is a recipe for silence.

This is the what I called the “simplest open problem in DCP optimization” in a recent post about DCP (Disease Control Priorities), but with more reflection, I should temper that claim. I’m not sure it is the simplest. I’m not sure it is an open problem. And I’m pretty sure that if we solve it, the DCP optimizers will come back with something more complicated.

But it is a nice, clean problem to start with. I’m calling it “Fully Stochastic Knapsack”. It looks just like the plain, old knapsack problem:
$\max \bigg\{ \sum_{i=1}^n v_ix_i \qquad s.t. \quad \sum_{i=1}^n w_ix_i \leq W, \quad x_i \in \{0,1\} \bigg\}$
The fully stochastic part is that everything that usually would be input data is now a probability distribution, and the parameters of the distribution are the input data.

This makes even deciding what to maximize a challenge. I was visiting the UW Industrial Engineering Dept yesterday, and Zelda Zabinsky pointed me to this nice INFORMS tutorial by Terry Rockafeller on “coherent approaches” to this.

Filed under combinatorial optimization, global health

## DCP MIP

(This is a post that I started a long time ago (Aug 10, 2010), but hung on to because it is only half-baked. But based on the philosophy that avoiding foolishness is a recipe for silence, I’m sending it out into the world. Coming next: the simplest useful open problem in DCP optimization.)

Acronyms are like candy in Global Health, and Operations Research is full of them, too. This post is a place for me to collect information about software available for solving the Mixed Integer Programming (MIP) problem that the Disease Control Priorities (DCP) project is going to put together.

DCP is a massive effort to quantify the cost-effectiveness of hundreds of health interventions across tens of “health platforms” (big hospitals, small clinics, pharmacies, etc). The output of this large, coordinated effort will be (as far as I’m concerned) a collection of giant matrices, that say, for different subsets of interventions across different platforms, (1) the cost of setting up the interventions, (2) the cost of operating the interventions, (3) the health gain from the interventions. Undoubtedly, there will be some quantification of the uncertainty in each of these quantities. Also, there is something called platform improvement, which can be thought of as a special type of intervention that makes a bunch of other interventions more effective on a certain platform. And there are a number of side-constraints; some interventions come together on certain platforms, some interventions are mutually exclusive, etc.

Some unknowns: (how) will the uncertainty in the entries of these matrices be quantified? Are the intervention choices all “yes/no” or do you choose how much you want of some of them, i.e a non-negative continuous variable?

This is the optimization that mixed integer programming was born for (except for the uncertainty, which takes us into less charted waters). So how we are going to do it, in theory, is just the sort of thing my OR classes focused on when I was in grad school. We didn’t talk much about how to do it in practice. Some of the hard-working students who sat in the business school and actually solved large integer programs would mutter about CPLEX once in a while at parties, but I didn’t pay it much heed.

Heed I must now pay. So I am collecting up the available MIP solvers here, and (eventually) evaluating them for my DCP optimization task. Got suggestions? I would love to hear them.

• Gurobi – 1 2 3
• ILOG/CPLEX – 1 2
• GAMS – 1
• AMPL – 1
• NEOS – 1


text:
Home > Macro, Phillips Curve > Okun’s Law

## Okun’s Law

Okun’s Law basically tells you how changes in output cause changes in unemployment.

Before when we’ve looked at the concept of the natural rate of unemployment we’ve talked about it in terms of the natural level of output.

The intuition has basically been:

– At the natural level of output, there is a certain number of workers who need to be employed to produce that output. So there is a natural rate of employment that corresponds to the natural level of output.

– If there is a natural rate of employment, there is obviously a corresponding natural rate of unemployment, eg if you need 95% of those eligible and searching for work to be employed to produce the natural level of output, then there will be a natural rate of unemployment of 5%.

– If output rises over the natural level of output, then you need more workers, so employment rate rises, and unemployment rate falls below the natural rate of unemployment. If output falls below the natural level of output then you need fewer workers so employment rate falls and unemployment rate rises above the natural rate of unemployment.

Okun’s Law tells you how output relates to unemployment. It isn’t a one for one relationship, unemployment responds less than one for one to changes in output. There are a few reasons for this:

1. In any firm, there are usually a set number of employees that the firm will need regardless of output. If a firm is in the construction industry, then when demand falls they might lay off builders and engineers because there is no work for them, but the finance department might still have roughly the same amount of work to do even though the figures don’t look as good. Equally if production expands, they will hire more builders and engineers and keep similar numbers in the finance department.

2. Recruitment costs are expensive anyway, so firms might engage in labour hoarding. This means that rather than just hiring and firing at will, when demand drops off, they might hold back before making too many redundancies, preferring to pay workers to not do much work, in the hope that demand will pick again quickly. If they make a lot of redundancies then not only are they paying redundancy payments but then will have to advertise, go through recruitment processes etc, when it picks up again, so if the fall in demand is short term that could end up more costly than just hanging on to workers in the first place. The more strict the redundancy laws in a country the more this is likely to happen. Labour hoarding is good in the sense that it means unemployment does not rise so much when there is a recession, but the flip side is that when the economy returns to growth, unemployment won’t fall so quickly because the firms can expand production without hiring more, because they had kept workers on the payroll anyway.

3. When the economy starts looking better, labour force participation increases. This means people who previously weren’t looking for work, start looking again. A good example of this is people coming out of higher education – when the economy is bad you get students going on to do Masters degrees or going off travelling rather than looking for work, so they don’t count on the unemployment figures, as the unemployment rate is given by the percentage of those looking for work who can’t find work, rather than just the percentage of the population who can’t find work. When the economy improves, more graduates will apply for jobs straight away rather than going on to postgrad degrees.

There’s another element that you have to factor in with Okun’s Law, it’s that the labour force tends to grow over time, as population grows, higher birth rates, immigration and so on. So in order to keep the natural rate of unemployment constant, you will need the natural level of output to be growing in proportion with labour force growth. This is why Okun’s Law doesn’t think in terms of a natural level of output but a normal growth rate of output.

Okun’s Law can be expressed in this form:

$u_t - u_{t-1} = -\beta (g_{yt} - \bar{g_y})$.

This is saying that the change in unemployment (unemployment in year t minus unemployment in year (t-1) )is equal to a negative parameter, $\beta$ which is less than one, which shows the responsiveness of unemployment to output, multiplied by the difference between output growth in year t and the normal growth rate of output. The parameter is negative because it is saying when output growth goes above the normal growth rate, then unemployment will fall. When output growth is below the normal growth rate, unemployment will rise. That means when output growth is on the normal growth rate then unemployment will be stable.

We can combine Okun’s Law with the Phillips Curve to get a relation between output and inflation.

The Phillips Curve equation was $\pi_t - \pi_{t-1} = -\alpha (u_t - u_n)$. We can rearrange Okun’s Law to $u_t =u_{t-1} -\beta (g_{yt} - \bar{g_y})$ and insert this into the Phillips Curve equation to get:

$\pi_t - \pi_{t-1} = -\alpha (u_{t-1} - u_n - \beta (g_{yt} - \bar{g_y}))$.

This gives us a relation between output and inflation.


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# Emissions from thaw ponds largely offset the carbon sink of northern permafrost wetlands

## Abstract

Northern regions have received considerable attention not only because the effects of climate change are amplified at high latitudes but also because this region holds vast amounts of carbon (C) stored in permafrost. These carbon stocks are vulnerable to warming temperatures and increased permafrost thaw and the breakdown and release of soil C in the form of carbon dioxide (CO2) and methane (CH4). The majority of research has focused on quantifying and upscaling the effects of thaw on CO2 and CH4 emissions from terrestrial systems. However, small ponds formed in permafrost wetlands following thawing have been recognized as hotspots for C emissions. Here, we examined the importance of small ponds for C fluxes in two permafrost wetland ecosystems in northern Sweden. Detailed flux estimates of thaw ponds during the growing season show that ponds emit, on average (±SD), 279 ± 415 and 7 ± 11 mmol C m−2 d−1 of CO2 and CH4, respectively. Importantly, addition of pond emissions to the total C budget of the wetland decreases the C sink by ~39%. Our results emphasize the need for integrated research linking C cycling on land and in water in order to make correct assessments of contemporary C balances.

## Introduction

Climate warming accelerates permafrost thaw in northern regions, leading to the breakdown and release of soil carbon (C) in the form of carbon dioxide (CO2) and methane (CH4)1. Northern permafrost wetlands are of particular importance due to their vast C stocks2, which are vulnerable to changes in climate3. Increases in ambient air temperatures will result in permafrost degradation and the release of stored C as CO2 and CH4, thus contributing to a positive feedback on the climate1. Degradation of permafrost and the ground slumping that follows can often cause shifts in vegetation composition and expansion of wet areas4,5 that may lead to the formation and growth of thaw ponds6,7. Thaw lakes and ponds have been suggested to play a particularly significant role in the permafrost C feedback loop by acting as direct conduits for the release of CO2 and CH4 to the atmosphere1,8,9. However, few in-depth pond studies exist, especially so regarding their quantitative importance for the C exchange between land and atmosphere. Freshwater lakes are well known to be significant emitters of CO2 and CH4 on a landscape scale10,11,12, but previous studies do not include empirical measurements from small thaw ponds. Here, we examined the importance of small ponds for C fluxes in permafrost wetlands in northern Sweden.

On a few occasions when C exchange between water and air has been measured in thaw ponds, they are frequently found to be high emitters of CO2 and CH47,13,14,15. The importance of thaw ponds, however, is largely overlooked in large scale assessments of C cycling due to their small size and the difficulties in mapping them using satellite imagery. For example, most upscaling studies exclude ponds smaller than 0.001 km2 16. Integrated studies in which direct C fluxes from small ponds in permafrost regions are included into a catchment-scale C balance are thus still lacking. This study is the first to directly include C exchange from small thaw ponds in a wetland C exchange estimate.

In this study, we quantified atmospheric C exchange from 52 small thaw ponds (surface area 4–150 m2) in two permafrost wetlands to determine their role in the total (terrestrial + aquatic) net carbon balance (NCB). Of the 52 ponds, we carried out high-resolution chamber measurements of CO2 and CH4 fluxes over the full growing season of 15 ponds with different vegetation composition, shoreline erosion, and water sources (for map of sampling locations see Supplementary Figure S1). Furthermore, we measured dissolved CO2 and CH4 of the other 37 thaw ponds to assess large-scale spatial patterns. The study location in northern Sweden is a representative of regions with high permafrost vulnerability. The study region is characterized by discontinuous permafrost that has been experiencing substantial thawing during the last decades, mainly attributed to changes in air temperature and precipitation17 (Fig. 1). Detailed assessments of one of the wetlands have observed an increased wetness between 1970 and 200018. By using aerial color imagery from 2008, we found that this trend has persisted alongside increases in annual air temperature and active layer thickness (Fig. 1). This change emphasizes the need to better quantify the role of ponds in the landscape C exchange.

## Results and Discussion

The results show strong oversaturation and high exchange of CO2 and CH4 to the atmosphere from the thaw ponds. The concentrations (mean ± standard error) of CO2 (467 ± 21 μM, n = 52) and CH4 (24 ± 3 μM, n = 52) are approximately an order of magnitude higher than the mean values reported for thaw ponds in northern Canada4 (means = 34 and 2 μM for CO2 and CH4, respectively), but are in the same range as permafrost ponds in west-central Siberia19 (range = 70–770 and 0.6–48 μM for CO2 and CH4, respectively). The average CO2 exchange measured from the ponds in our study (279 ± 58 mmol C m−2 d−1) was greater than exchanges (max = 114 mmol C m−2 d−1) reported from thaw ponds in northern Canada7 and from lakes (average value 15 mmol C m−2 d−1) in the same catchment as in this study20. The mean diffusive CH4 exchange (7 ± 0.2 mmol C m−2 d−1) in the ponds was among the highest diffusive CH4 fluxes reported, but was the same magnitude as found in ponds in eastern Siberia (average = 4 mmol C m−2 d−1)14. Ebullition was highly variable between lakes and accounted for 71% the total CH4 flux when observed (17 ± 6 mmol C m−2 d−1).

Four pond types were identified during this study-including open water, moss-dominated, sedge-dominated, and lake-fed ponds (Supplementary Figure S2). Both CH4 and CO2 varied widely throughout the growing season and pond types showed different temporal variation. There were not significant differences in ebullition fluxes between pond types (Mann-Whitney U Statistical test, p-value = 0.44). Open-water systems had the highest mean diffusive emissions for both CO2 (610 ± 69 mmol C m−2 d−1) and CH4 (14 ± 2 mmol C m−2 d−1; Mann-Whitney U Statistical test, p-value < 0.001; Fig. 2b,d). These ponds had little to no vegetation at the surface or on the bottom and were surrounded by eroding banks, characteristics associated with high C exchange from ponds in northern Canada7. While this study was not designed to assess the importance of various drivers of C dynamics across ponds, the relatively high diffusive fluxes from open water ponds could be a result of high gas exchange velocities, relatively low photosynthetic CO2 fixation, and high terrestrial input of C and organic matter from adjacent thawing and eroding soils compared to vegetated ponds.

A critical question is to what degree the emissions from thaw ponds are of quantitative importance compared to the overall C exchange from permafrost wetlands. One of the wetlands in this study (Stordalen) has been subject to extensive C exchange studies by chamber and eddy covariance techniques, enabling the first estimate of a complete NCB of a permafrost wetland and the specific importance of thaw ponds. Earlier studies in Stordalen found that the entire wetland is a large sink for CO2 and a source of CH421,22. However, these studies focused mainly on the terrestrial or vegetated (non-open water patches) wetland and did not measure ponds directly. To incorporate the C emissions from ponds in our study into the NCB for the entire wetland, we combined our data with the mean terrestrial C exchange over the green season from 2002 to 2007 from Bäckstrand et al.21, and the areal coverage of open water ponds (0.43 ha) and the vegetated wetland (16.5 ha) in 2008. In the study by Bäckstrand et al.22, based on automated chamber measurements, terrestrial wetland components were divided into dry palsa, sphagnum, and wet/minerotrophic eriophorum patches. While their C-budget for the wetland includes wet areas, it does not include diffusive emission estimates for ponds specifically. The addition of the pond C emissions from 2015 to the NCB increased the CH4 source and decreased the CO2 sink (Fig. 3). The overall NCB, including both CO2-C and CH4-C, decreased from −44 kg C d−1 to −27 kg C d−1. We do note that C fluxes are dependent on multiple physical parameters and these parameters are not exactly the same between 2000 and 2015.

Although the C emission from the thaw ponds are of quantitative importance, the exact contribution should be treated with caution given the uncertainty in area of ponds. We estimated a range in contribution (Fig. 3) of thaw ponds to the NCB by using the area of ponds in 2000 (~1%)18 and 2008 (~2.5%). It is highly likely that the ponds now occupy an even larger percentage of the wetland landscape due to further permafrost thaw and saturated hollow development23, however images from this study’s research season were not available. Assuming pond developing continuous to follow the trend observed between 2000 and 2008 (1.5% increase), total pond area in 2015 can be estimated to be around 4%. At 4% of the total land cover, C emissions from ponds would reduce the NCB from ~−27 kgC d−1 to only ~−3 kgC d−1. Additionally, available images used for upscaling in this study only identify open-water ponds and do not distinguish vegetated ponds from the surrounding terrestrial vegetation; therefore, we only use open-water emission means in the upscaling estimate. Not including vegetated ponds is most likely a conservative estimate of the NCB. To upscale C emissions from small ponds and improve estimates of larger scale NCB of high latitude peatland regions, there is a need for higher resolution areal data and improved techniques to estimate the areal C contribution from different ponds in the landscape.

## Conclusion

Our results suggest that ponds in northern permafrost wetlands are considerable sources of C to the atmosphere, significantly offsetting the net C uptake of wetlands, and thus reducing overall atmospheric C sink strength of the landscape. Thaw ponds cover a significant portion of land in the north6, and it is likely that those systems represent an important and sensitive component of the permafrost carbon feedback loop. The role of ponds as hotspots for C exchange following permafrost thaw and subsequent pond formation may be of increasing importance in permafrost regions in future decades following predicted permafrost thaw6. While projecting the trajectory of pond development and C exchange is highly uncertain, pond coverage may even decrease in some regions following thawing24,25, our results suggest that C release from thaw ponds following permafrost thaw may strongly contribute to a decrease in the overall C sink capacity of northern wetlands (Fig. 4). To reduce uncertainties, there is a need for more integrated research and further experiments or manipulations that focus on incorporated small ponds into regional NCB.

Importantly, the type of pond and the vegetation that it is comprised of may be a driving factor. If ponds develop into sedge-dominated or deeper, open-water systems, more C may be released to the atmosphere. Vegetation shifts in this direction have already been observed during naturally induced permafrost thaw17,18 and experimentally due to increased snow cover26. However, if there is a trend towards moss-dominated ponds, atmospheric C emissions could be substantially less. Understanding and quantifying the C emissions from the different types of ponds is crucial to predicting and modeling future emissions from permafrost wetlands subject to thawing since the ponds are constantly changing and evolving. Our results emphasize the need for integrated research linking C cycling on land and in water to make correct assessments of contemporary and future C balances.

## Methods

### Site description

Sampling took place in two wetland complexes over the duration of the growing season (June-October) in 2015. The Stordalen (68 N, 19 E) and Storflaket (68 N, 19 E) wetlands are located in the same catchment, approximately 3 km apart, in a discontinuous permafrost zone east of Abisko, Sweden. Stordalen covers ~15 km2 and Storflaket ~3 km2. The wetland complexes contain raised patches of peat underlain by permafrost, which are surrounded by saturated hallows and ponds. The hollows are comprised of graminoids (Carex sp., Eriophorum sp.) and sphagnum sp., while the palsas are covered by woody shrubs (eg Betula nana), evergreen shrubs (eg, Andromeda polifolia, Empetrum hermaphroditum), moss (Sphagnum sp.) and lichen. The active layer thickness is approximately 0.5 m in the palsas and 1–3 meters in the hallows at both sites17. Yearly temperature and precipitation means for this region were recorded at the nearby Abisko Scientific Research Station (http://www.polar.se/abisko).

### Ponds

In total, we sampled 52 ponds. Six ponds in Storflaket and nine ponds in Stordalen were sampled twice a week from the end of June until ice cover in early October. An additional 37 ponds were sampled in July. The ponds were chosen to cover a variety of morphologies, vegetation types, and degrees of erosion along the shoreline. Ponds were classified into moss dominated, sedge dominated and open water based on within-pond (1 × 1 meter grid) surface vegetation composition using a cluster analyses (R Company 3.2.1, pvclust Package). We also separated lake fed ponds that occasionally received external inputs of water from nearby lake.

### Water sampling and analysis

Water temperature, dissolved oxygen, and barometric pressure were measured in situ four times a week using a YSI Professional Optical Dissolved Oxygen instrument (Yellow Springs Instruments, Ohio, USA), which was calibrated at the start of each week. Surface water samples were collected weekly in 0.5 L containers, pre-rinsed in the field with pond water. Samples were filtered the same day in the laboratory (Sarstedt Filtropur S 0.45 mm), acidified (DOC) thereafter refrigerated (DOC) until processing. Conductivity and pH were analyzed in the laboratory on the same day as sampling (MP220, Mettler Toledo International Inc.). Dissolved inorganic carbon (DIC) and dissolved CH4 samples were collected from the surface of the water twice a week using a five mL plastic syringe. Using a headspace method, 4 mL of water was injected into a pre-prepared, 22 mL vial (Wheaton) with 20 uL of 20% HCL27. Vials were stored in an upside down position at room temperature until analysis. Methane and DIC concentrations were determined using a gas chromatograph with a methanizer and flame-ionization detector (Clarus 500, Perkin Elmer Inc. U.S.). Internal standards were prepared with each batch of samples to correct for possible leakage of gas over time. Filtered DOC samples were run on a Shimadzu TOC-V CPH analyzer (Shimadzu Corporation, Japan).

Dissolved CO2 concentrations were measured twice a week using a Vaisala sensor attached to a handheld logger (Helsinki, Finland, GMM220 and GM70 series). Sensors were deployed at the water’s surface and were occasionally stirred until the concentration hit equilibrium (5–30 minutes). Concentrations were later back calibrated in the laboratory to correct for temperature and pressure settings28.

### Carbon dioxide fluxes

Carbon dioxide fluxes were measured twice a week at seven of the fifteen ponds using a floating chamber (volume = 10.9 L). A plastic chamber was equipped with a CO2 sensor and attached by rope to a pole and handheld data logger (Vaisala Inc. Helsinki, Finland, GMM220 and GM70 series). The chamber was floated on the surface of the water between 9 am and 3 pm for 5–10 minutes at each pond while the concentration was recorded. Using the linear change in concentration and the dimensions of the chamber, the flux (F) was estimated using equation 1:

$$F=\frac{Vch\times S\times Kh\times P\times Q}{A}$$
(1)

where Vch is the volume of the chamber (m3), A is the area of the chamber (m2), S is the linear change in concentration measured over the five-minute period (ppm/min), Kh is Henry’s law constant (dependent on temperature), P is the pressure (atm), and Q is a conversion factor to set the flux units to mmol Cm−2 d−1. To calculate the flux of CO2 from the ponds that were not directly measured with a chamber, we used the concentration of dissolved CO2 and a variation of Fick’s law (eq. 2) to determine the piston velocity coefficient (k):

$$F=k(Cw-Ca)$$
(2)

which can be rearranged to solve for k as:

$$k=\frac{F}{(Cw-Ca)}$$
(3)

where F is the chamber flux (umol Cm−2 d−1), Cw is the concentration of dissolved gas at equilibrium with the headspace (umol Cm−3) and Ca is the concentration of CO2 in the atmosphere. All dissolved gas concentrations (CO2 and CH4) were calculated using Henry’s law:

$$Ga{s}_{aq}=Kh\times pGAS$$
(4)

where pGAS is the partial pressure of the gas in the headspace (ppm). The calculated k for both CO2 and CH4 values were normalized to 20 °C by calculating k600 values29.

### Methane fluxes

A 24-hour static chamber (volume = 10.9 L) flux method was used to measure total CH4 emissions at each pond30. Flux measurements were taken on a biweekly schedule. To separate the contributions of ebullition events from the diffusive flux, we looked at the distribution of the experimentally derived k600 values from the CO2 chamber flux measurements. Measured CH4 fluxes with k600 values above the mean CO2 k600 value (0.79 m d−1) were not considered in the diffusive flux calculations. A total of 22% (61 of 280) measurements were determined to be effected by ebullition (based on k600 > 0.79 m d−1) and ebullition were estimated by subtracting the average diffusive flux from the total flux of ebullition-impacted chambers30. Given that ebullition is highly sporadic and spatially heterogeneous, we reported ebullition as a mean rate.

### Statistics

Statistical analyses were done using the R statistics package (3.2.2, The R Company). Both CO2 and CH4 fluxes were normally distributed, however, the variances and sample sizes between pond types and monthly fluxes were not the same, therefore, we used the Kruskal-Wallis test for multiple group analyses and the Mann-Whitney U tests for follow-up pair-wise comparisons (p < 0.05). K600 values for CO2 and CH4 showed similar distributions.

### GIS Analysis and Carbon Budget Estimate

Pond area within Stordalen was calculated using ArcGIS software (esri. ArcGIS Desktop. 10.1 Redlands, CA). We used a mosaic of real-color images (8 × 8 cm resolution) of Stordalen mire taken in August 2008. The mosaic was clipped to represent the same area as presented in Malmer et al.18 and as used in Bäckstrand et al.21. Then, digital classification of open water ponds was determined with the help of user-selected training locations. Once training sites were selected, we used supervised classification to identify all open water ponds in the mire. We then used the pixel count of all areas classified as a pond to determine the total pond area in the mire.

To incorporate C emissions from ponds into the terrestrial NCB for the wetland, we used pond flux measurements from Storflaket and Stordalen and terrestrial flux values reported in Bäckstrand et al.21. In this study, the wetland was split into dry palsa, sphagnum, and wet/minerotrophic eriophorum components. Fluxes were measured from these patch types over a period of 7 years. The average emission rates from each land-cover type and the average number of growing days over the 7-year period were used in our estimate of total C loss and uptake from the terrestrial components of the mire. Importantly, while Bäckstrand et al.’s C-budget for the wetland includes wet areas, it does not include fluxes from open patches of water. Here we included both diffusive and ebullition fluxes in the previous NBC estimate by multiplying the mean daily flux from our study for both CO2 and CH4 from open-water ponds with the total pond area of the wetland. Total CO2 and CH4 emissions over the growing season (averaged from the previous 7 year data set) from the ponds were then added to total C emission and uptake estimates for the terrestrial components of the mire. Only fluxes and areas of open water ponds were included in upscaling due to difficulties associated with separating moss and sedge dominated ponds from wet, minerotrophic patches in the aerial image.

### Data availability

Data are available upon request.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

Support for this work was funded by the Fulbright US Student Grant and the Climate Impacts Research Centre. We thank Kalle Heuchel, Albin Bjärhall, Keith Larson, and Anders Jonsson, for help with fieldwork and laboratory analyses. Thank you to the Abisko Scientific Research Station for supplying weather data and for use of the facilities.

## Author information

### Affiliations

1. #### Department of Renewable Resources, University of Alberta, 116 St & 85 Ave, Edmonton, AB, CA, T6G 2R3, Canada

• McKenzie Kuhn
2. #### Climate Impacts Research Centre (CIRC), Department of Ecology and Environmental Science, Umeå University, SE-901 87, Umeå, Sweden

• McKenzie Kuhn
• , Erik J. Lundin
• , Reiner Giesler
•  & Jan Karlsson
3. #### Department of Physical Geography and Ecosystem Science, Lund University, Sölvegatan 12, 223 62, Lund, Sweden

• Margareta Johansson
4. #### Swedish Polar Research Secretariat, Abisko Scientific Research Station, SE-981 07, Abisko, Sweden

• Erik J. Lundin

### Contributions

J.K. and M.K. designed the study; M.J. contributed data; M.K. performed fieldwork; E.L., M.K. did laboratory work; M.K., E.L., R.G., and J.K. analyzed and interpreted the data; and M.K., J.K., M.J., E.L., and R.G. contributed to the manuscript.

### Competing Interests

The authors declare no competing interests.

### Corresponding author

Correspondence to McKenzie Kuhn.


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# Create A UWidget At Runtime

UE4’s built-in blueprint function ‘CreateWidget’ only allows you to specify UUserWidgets, so to add something basic like a button, border or text at runtime, you have to create a custom UUserWidget to wrap it - very inefficient. Luckily, there’s a ConstructWidget() function in C++ that can easily be exposed to blueprints.

Make sure you’ve got a BP/C++ project, then create a blueprint function library C++ class.

## Code

Add this to the .h file:

	/*
Creates a base UWidget (text, border, image, etc) at runtime.
*/
UFUNCTION(BlueprintCallable, Category = "UMG")
static UWidget* CreateUWidget(UUserWidget *InWidget, TSubclassOf<UWidget> WidgetToCreate);

And this to the .cpp:

UWidget * UWidgetFunctions::CreateUWidget(UUserWidget * InWidget, TSubclassOf<UWidget> WidgetToCreate)
{
if ((!InWidget) || (!WidgetToCreate))
{
return nullptr;
}

UWidget *CreatedWidget = InWidget->WidgetTree->ConstructWidget<UWidget>(WidgetToCreate);
return CreatedWidget;
}

It works the same as CreateWidget, in that you’ll need to add it to something after creation, in the same UUserWidget that it was created in (InWidget). So you’ll normally use it like this:

## Videogames

Hey, do you like videogames? If so check out my game Grab n' Throw on Steam, and add it to your wishlist. One gamemode is like dodgeball crossed with soccer except instead of balls you throw stacks of your own teammates. Another is like golf but on a 16x16km landscape with huge throw power to match. And there's plenty of others to come!

See full gameplay on Steam!


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Q

# Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x

15.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):  $\csc x \cot x$

Views

Given,

$f(x)=\csc x \cot x$

the Multiplication property of derivative,

$\frac{d(y_1y_2)}{dx}=y_1\frac{dy_2}{dx}+y_2\frac{dy_1}{dx}$

Applying the property

$\frac{d(\csc x)(\cot x))}{dx}=\csc x\frac{d\cot x}{dx}+\cot x\frac{d\csc x}{dx}$

$\frac{d(\csc x)(\cot x))}{dx}=\csc x(-\csc^2x)+\cot x(-\csc x \cot x)$

$\frac{d(\csc x)(\cot x))}{dx}=-\csc^3x-\cot^2 x\csc x$

Hence derivative of the function is $-\csc^3x-\cot^2 x\csc x$.

Exams
Articles
Questions


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# Pre Algebra

how do you make a decimal into a fraction?

1. 👍
2. 👎
3. 👁
1. Divide the top number by the bottom number. For example 1/2, divide 1 by 2 and you get 0.50.

1. 👍
2. 👎
2. for the numerator write down the digits of the decimal number without the decimal.
For the denominator put down a 1 followed by as many zeros as you had decimal places. Reduce the fraction to lowest terms if needed.

e.g. .567 = 567/1000

1.24 = 124/100 = 31/25 or 1 6/25

1. 👍
2. 👎

## Similar Questions

1. ### One Last Help

1. 423% as a decimal a. 0.423 b. 42.3 c. 4.23 (GOT THIS) d. 423 2. 4 1/4 as a percent a. 4.20% b. 4.25% (Debating on this or...) c. 420% d. 425% (...this.) 3. 120% as a fraction a. 1 1/5 (GOT THIS) b. 3/25 c. 1 3/25 d. 1 1/2 4.

2. ### Math

How do you write 24% as a decimal? 2.4 0.24*** 0.024 How do you write 135% as a decimal? 1.35*** 13.5 0.135 How do you write 4% as a decimal? 0.4*** 0.40 0.04 Which fraction is equivalent to 72%? (No answer, not sure on this one.)

3. ### Helpppppp

Use benchmarks to estimate the sum. three-fifths+start fraction 3 over 17 end fraction A. 2 B. one-half C. 1 D. 0 Estimate the difference. 6five twelvths – 4one ninth A. 2 B. 3 C. 1 D. 4 Estimate the product. 6four

4. ### Math

What is 5/9 written as a decimal? 0.45 0.4 repeating 0.5 0.5 repeating What is 0.26 written as a fraction in simplest form? 26 over 100 13 over 50 26 over 10 13 over 25 In a fraction with a denominator of 15,which value could the

1. ### Math~Fractions ans decimals

1. Write the fraction or mixed number as a decimal. 7/8 0.78 0.875* 0.8777 1.875 2. Write the fraction or mixed number as a decimal 1 1/2 0.50 1.5* 1.05 1.1 3. Write the fraction or mixed number as a decimal. 4 3/8 0.375 4.35

2. ### unt

A coin is tossed 9 times. What is the probability of getting all heads? Express your answer as a simplified fraction or a decimal rounded to four decimal places.

3. ### Math

1.In a fraction with a denominator of 15, which value could the numerator be to produce a repeating decimal? A. 15 B. 9 C. 11 D. 12•• 2.Which of the following is an example of a nonterminating, nonrepeating decimal? a

4. ### math

Jade used Fraction 3 over 4 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 4 over 5 yards of fabric, and why? (1 point) No, because the quotient of Fraction 3 over 4 division sign Fraction 1

1. ### Math

If one hundredth is divided into ten equal parts, each part represents one what? 1- decimal, 2- decimal point, 3- fraction, or 4- thousandth.

2. ### plz helpppppppp

Use benchmarks to estimate the sum. three-fifths+start fraction 3 over 17 end fraction A. 2 B. one-half C. 1 D. 0 Estimate the difference. 6five twelvths – 4one ninth A. 2 B. 3 C. 1 D. 4 Estimate the product. 6four

3. ### math help ms sue please

Which sum will be irrational? (1 point) 3 + 2 start root 19 end root plus start fraction 7 over 2 end fraction Start Fraction 18 over 3 End Fraction plus Start Fraction 11 over ten thousand End Fraction. –6 + (–3.251) Which

4. ### MATH

I had to change this fraction to a percent: 1 1/5= 120% Is this correct? To get this answer I changed the fraction 1 1/5 to a decimal, 1.2, then I moved the decimal two places to the right, making it 120%. Please tell me if I have


text:
# Abel equation of the first kind

In mathematics, an Abel equation of the first kind, named after Niels Henrik Abel, is any ordinary differential equation that is cubic in the unknown function. In other words, it is an equation of the form

$y'=f_3(x)y^3+f_2(x)y^2+f_1(x)y+f_0(x) \,$

where $f_3(x)\neq 0$. If $f_3(x)=0$ and $f_0(x)=0$, or $f_2(x)=0$ and $f_0(x)=0$, the equation reduces to a Bernoulli equation, while if $f_3(x) = 0$ the equation reduces to a Riccati equation.

## Properties

The substitution $y=\dfrac{1}{u}$ brings the Abel equation of the first kind to the "Abel equation of the second kind" of the form

$uu'=-f_0(x)u^3-f_1(x)u^2-f_2(x)u-f_3(x). \,$

The substitution

\begin{align} \xi & = \int f_3(x)E^2~dx, \\[6pt] u & = \left(y+\dfrac{f_2(x)}{3f_3(x)}\right)E^{-1}, \\[6pt] E & = \exp\left(\int\left(f_1(x)-\frac{f_2^2(x)}{3f_3(x)}\right)~dx\right) \end{align}

brings the Abel equation of the first kind to the canonical form

$u'=u^3+\phi(\xi). \,$

Dimitrios E. Panayotounakos and Theodoros I. Zarmpoutis discovered an analytic method to solve the above equation generally.[1]

## Notes

1. ^ E. Panayotounakos, Dimitrios; Theodoros I. Zarmpoutis (29 August 2011). "Construction of Exact Parametric or Closed Form Solutions of Some Unsolvable Classes of Nonlinear ODEs (Abel's Nonlinear ODEs of the First Kind and Relative Degenerate Equations)". International Journal of Mathematics and Mathematical Sciences Volume 2011 (2011) 2011: 13. doi:10.1155/2011/387429. PMID 387429.


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# 100 oranges are bought at the rate of Rs.350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is

$\par&space;C.P.&space;of&space;1&space;orange&space;=&space;Rs.$ $\left(\frac{350}{100}\right)&space;=$  $\par&space;Rs.&space;3.50$

$\par&space;S.P.&space;of&space;1&space;orange&space;=&space;Rs.$ $\left(\frac{48}{12}\right)&space;=$  $\par&space;Rs.&space;4$

$\par&space;Gain\%&space;=$ $\left(\frac{0.50}{3.50}\times&space;100)\right)\%$  $=&space;\frac{100}{7}\%&space;=$ $14\frac{2}{7}\%$


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# [Xy-pic] xypic bug

Michael Barr barr@barrs.org
Sat, 1 Dec 2001 07:39:41 -0500 (EST)

It is definitely a bug.  Kris Rose is now gainfully employed and rarely
in his unreleased version the bug is fixed.  But he didn't reply when I
asked him about releasing it.  Meantime, the way around it is to keep
those intersecting lines short.  That is, piece them together from shorter
segments.  I don't recall, but there may be an example of this in my
documentation to diagxy, which is a front end for xypic.  The latest
version is available at ftp.math.mcgill.ca/pub/barr/diagxy.zip.

Michael Barr

> Date: Fri, 30 Nov 2001 12:17:09 -0600 (CST)
> From: James Borger <borger@math.uchicago.edu>
> To: <xy-pic@tug.org>
> Subject: [Xy-pic] bug?
>
>
> Dear xy-pic-ers,
>
> I've found what appears to be a bug in the way xy-pic handles
> intersections of lines.  That said, I have pretty limited experience with
> xy-pic, so the bug could easily be in me.
>
> I want to typeset a three-dimensional commutative diagram and have some
> lines appear to pass under others.  The problem is that sometimes xy-pic
> draws only one of the two pieces of the lower line, which should be
> broken.  I had this problem once before and was able to work around it by
> changing things that I though should have no effect on the output.
> Unfortunately, I didn't save that example.
>
> The misbehaving (LaTeX) code is below (in simplified form).  The arrow
> from J to K is the offending one.
>
> Best,
>
> Jim Borger
>
> =======================================================================
>
> \documentclass{amsart}
> \usepackage{amscd, amssymb}
> \usepackage[all]{xy}
>
> \begin{document}
>
> $> \begin{xy} <0pt,0pt>;<16mm,0mm>:<0mm,-7mm>:: > (2,0) *+{A}="a", > (5,0) *+{B}="b", > (2,3) *+{C}="c", > (5,3) *+{D}="d", > (0,4) *+{E}="e", > (2,6) *+{F}="f", > (5,6) *+{G}="g", > (0,7) *+{H}="h", > (3,7) *+{I}="i", > (1,8) *+{J}="j", > (4,8) *+{K}="k", > (0,10) *+{L}="l", > (3,10) *+{M}="m", > \ar "a";"b" > \ar "c";"a" > \ar "d";"b" > \ar "e";"a" > \ar "f";"c" > \ar "f";"g" |!{"i";"d"}\hole > \ar "g";"d" > \ar "h";"e" > \ar "h";"i" > > \ar "i";"d" > \ar "f";"j" |!{"h";"i"}\hole > \ar "j";"k" |!{"m";"i"}\hole > \ar "k";"g" > \ar "l";"j" > \ar "l";"h" > \ar "l";"m" > \ar "m";"i" > \ar "m";"k" > \end{xy} >$
>
> \end{document}


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Legend ‘-DynamicLegend’ semi-documented feature

In one of my projects, I had to build a GUI in which users could interactively add and remove plot lines from an axes. The problem was that the legend needed to be kept in constant sync with the currently-displayed plot lines. This can of course be done programmatically, but a much simpler solution was to use legend‘s semi-documented ‘-DynamicLegend’ feature. Here’s a simple example:

x=0:.01:10; plot(x, sin(x), 'DisplayName','sin'); legend('-DynamicLegend');   hold all; % add new plot lines on top of previous ones plot(x, cos(x), 'DisplayName','cos');

We can see how the dynamic legend automatically keeps in sync with its associated axes contents when plot lines are added/removed, even down to the zoom-box lines… The legend automatically uses the plot lines ‘DisplayName’ property where available, or a standard ‘line#’ nametag where not available:

Dynamic legend

DynamicLegend works by attaching a listener to the axes child addition/deletion callback (actually, it works on the scribe object, which is a large topic for several future posts). It is sometimes necessary to selectively disable the dynamic behavior. For example, in my GUI I needed to plot several event lines which looked alike, and so I only wanted the first line to be added to the legend. To temporarily disable the DynamicLegend listener, do the following:

% Try to disable this axes's legend plot-addition listener legendAxListener = []; try legendListeners = get(gca,'ScribeLegendListeners'); legendAxListener = legendListeners.childadded; set(legendAxListener,'Enable','off'); catch % never mind... end   % Update the axes - the legend will not be updated ...   % Re-enable the dynamic legend listener set(legendAxListener,'Enable','on');

Unfortunately, this otherwise-useful DynamicLegend feature throws errors when zooming-in on bar or stairs graphs. This can be replicated by:

figure; bar(magic(4)); %or: stairs(magic(3),magic(3)); legend('-DynamicLegend'); zoom on; % Now zoom-in using the mouse to get the errors on the Command Window

The fix: modify %MATLABROOT%\toolbox\matlab\scribe\@scribe\@legend\init.m line #528 as follows:

%old: str = [str(1:insertindex-1);{newstr};str(insertindex:length(str))];   %new: if size(str,2)>size(str,1) str=[str(1:insertindex-1),{newstr},str(insertindex:length(str))]; else str=[str(1:insertindex-1);{newstr};str(insertindex:length(str))]; end

The origin of the bug is that bar and stairs generate hggroup plot-children, which saves the legend strings column-wise rather than the expected row-wise. My fix solves this, but I do not presume this solves all possible problems in all scenarios (please report if you find anything else).

Semi-documented

The DynamicLegend feature is semi-documented. This means that the feature is explained in a comment within the function (which can be seen via the edit(‘legend’) command), that is nonetheless not part of the official help or doc sections. It is an unsupported feature originally intended only for internal Matlab use (which of course doesn’t mean we can’t use it). This feature has existed many releases back (Matlab 7.1 for sure, perhaps earlier), so while it may be discontinued in some future Matlab release, it did have a very long life span… The down side is that it is not supported: I reported the bar/stairs issue back in mid-2007 and so far this has not been addressed (perhaps it will never be). Even my reported workaround in January this year went unanswered (no hard feelings…).

DynamicLegend is a good example of a useful semi-documented feature. Some other examples, which I may cover in future posts, include text(…,‘sc’), drawnow(‘discard’), several options in pan and datacursormode etc. etc.

There are also entire semi-documented functions: many of the uitools (e.g., uitree, uiundo), as well as hgfeval and others.

Have you discovered any useful semi-documented feature or function? If so, then please share your finding in the comments section below.

Related posts:

1. Multi-column (grid) legend This article explains how to use undocumented axes listeners for implementing multi-column plot legends...
2. Undocumented feature list A list of undocumented MATLAB features can be retrieved. Here's how... ...
3. Transparent legend Matlab chart legends are opaque be default but can be made semi- or fully transparent. ...
4. Undocumented feature() function Matlab's undocumented feature function enables access to some internal experimental features...
5. Plot performance Undocumented inner plot mechanisms can be used to significantly improved plotting performance...
6. Context-Sensitive Help Matlab has a hidden/unsupported built-in mechanism for easy implementation of context-sensitive help...

 Print

17 Responses to Legend ‘-DynamicLegend’ semi-documented feature

1. Thanks for this tip.
I was in a similar need, and was getting the legend cell via get, appending the new string, and setting the cell back.

leghandle = findall(gcf, 'tag', 'legend'); legstr = get(leg,'String'); % ensure legstr is a cell, not a string if ischar(legstr), legstr = mat2cell(legstr); end legstr(end+1) = {'New legend string'};

This seems much simpler.

2. Pietro says:

I was looking for an undocumented matlab feature named ‘feature’ and google luckied me here. Maybe you know something about. I tried

which feature

and I found out this ‘feature’ is an undocumented built-in function.

How I got across it?

I typed configinfo.m M-file attached to Matlab white paper on performance.

Nice blog, useful even for a beginner in Matlab as I am.

• Yair Altman says:

Thanks Pietro.

I plan to write a post about some of feature‘s features in the future. Keep a look-out for this on this blog. You can see this in my TODO list.

So much to do, so little time…

Yair

3. Pingback: uitree | Undocumented Matlab

4. Stephan says:

I was searching for a way to use a legend’s “refresh” function (that is available when right-clicking on the legend with the mouse) in a script. When I came across this post I first thought this was the way Matlab implemented the “refresh” functionality.
However, ‘DynamicLegend’ only seems to react to additions or deletions to the axes: switching the ‘Visibility’ of a line to ‘off’ or switching the legend entry off by

set(get(get(line_handle,'Annotation'),'LegendInformation'),'IconDisplayStyle','off')

is ignored by the ‘DynamicLegend’ feature. The “refresh” function correctly removes the corresponding legend entry in these cases.
Do you know how to use “refresh” from the command line?

• @Stephan – yes: You can access the Refresh uicontextmenu item (and any other context-menu item) directly from the legend axes, and then run it via the hgfeval function, as follows:

hLegend = findall(gcf,'tag','legend'); uic = get(hLegend,'UIContextMenu'); uimenu_refresh = findall(uic,'Label','Refresh'); callback = get(uimenu_refresh,'Callback'); hgfeval(callback,[],[]);

For the record, this invokes the refresh_cb function within %matlabroot%/toolbox/matlab/scribe/@scribe/@legend/methods.m. You can place a breakpoint there to see exactly what it does internally.

5. Andy says:

I got the same Problem/Question as Stephan I do plot all data in the Fig however only some data is visible but in the legend all data even the one not visible is listed. Only by right klick an refresh I can get rid of them however I can’t do that with every single file….

Hope there will be a solution in the future.

• @Stephan and @Andy – the Legend’s DynamicLegend functionality only listens to newly-created axes children (in %matlabroot%/toolbox/matlab/scribe/@scribe/@legend/init.m line 102 [for R2012aPR]), and axes children deletions (in %matlabroot%/toolbox/matlab/scribe/@scribe/@legend/methods.m line 1281 [R2012aPR again]).

It should be relatively easy to modify any of these two places to listen to changes in the Visible property of axes children. I described the mechanism for doing this in several articles (here for example).

6. sunny says:

wow, i never knew there was a function like this and i have been thinking on how to program it. thanks, this is gonna save me lots of time

7. Teodor says:

Hi. Thank you for this post. At the moment I am a bit stuck as trying to get the ‘ScribeLegendListeners’ throws a ‘MATLAB:class:InvalidProperty’ exception. There seem to be no such property…

My University is using Matlab-R2011a. Could it be something related to their installation?

What I am doing is using -DynamicLegend for plotting data in multiple iterations. However, I need to remove from the legend some plotted lines.

Could you recommend other solutions? Thank you.

• @Teodor – try placing a drawnow after plotting the lines and before trying to access the hidden ScribeLegendListeners property. It is also possible that you are trying to access this property on a handle of another object (maybe one of the line plots, or a figure, or another axes), rather than the handle of the axes that holds the plots for the requested legend.

8. Pingback: treeTable | Undocumented Matlab


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# Chemical Equilibrium - finding equilibrium constant given degree of dissociation

$\ce{N2O4}$ is dissociated $20\ \%$ at 27 degrees Celsius and 1 bar. Find the equilibrium constant of that reaction. What percentage of $\ce{N2O4}$ dissociates at $13.15\ \mathrm{kPa}$?

An explanation of the solution is below, but there are two things I do not understand.

Why do we have $1 + \alpha$ in the denominator in equations ${\text(6)}$–${\text(9)}$?

How do we get the fraction $\dfrac{(2\alpha)^2}{1-\alpha}$ in equation $\text{(11)}$?

If the degree of dissociation is $\alpha$, then the amounts of substances present $n_0$ dissociated is $n_0 \alpha$, and the remaining amount of undissociated substance $n_0 (1-\alpha)$. Since each molecule $\ce{AB}$ dissociates into molecules of $\ce{A}$ and $\ce{B}$, the amounts of each substance is \begin{align} n_{\ce{A}} &= n_{\ce{B}} = n_0 \cdot \alpha \tag{1}\\ n_{\ce{AB}} &= n_0 \cdot (1-\alpha) \tag{2} \end{align} In the case of the dissociation of dinitrogen tetroxide, $\ce{N2O4}$, it will be \begin{align} n_{\ce{A}} &= 2n_0 \alpha \tag{3}\\ n_{\ce{AB}} &= n_0 \cdot (1-\alpha) \tag{4}\\ \sum{n} &=n_0 (1+\alpha) \tag{5}\\ x_{\ce{A}} &= \dfrac{2\alpha}{(1+\alpha)} \tag{6}\\ x_{\ce{AB}} &= \dfrac{1-\alpha}{1+\alpha} \tag{7}\\ x_{\ce{NO2}} &= \dfrac{2\alpha}{(1+\alpha)} =\dfrac{0.40}{1.20}=0.3333 \tag{8}\\ x_{\ce{N2O4}} &= \dfrac{1-\alpha}{1+\alpha}=\frac{0.80}{1.20}=0.6666 \tag{9}\\ K_p &= \dfrac{(P_{\ce{NO2}})^2}{P_{\ce{N2O4}}}=P\cdot \dfrac{( x_{\ce{NO2}})^2}{ x_{\ce{N2O4}}} = \mathrm{ 1\ bar \cdot \dfrac{(0.3333)^2}{0.6666} = 0.1667\ bar} \tag{10} \end{align} We obtain the degree of dissociation of $\ce{NO2}$ at a pressure of $13.15\ \mathrm{kPa}$: $$\dfrac{K_p}{P} = \dfrac{(2\alpha)^2}{(1-\alpha)}=\mathrm{\dfrac{0.1667\ bar}{0.1315\ bar}=1.268} \tag{11}$$ From here, we get: $$4\alpha^2 = 1.268 (1-\alpha) = 1.268 -1.268\alpha \tag{12}$$ Which becomes $$4\alpha^2 =1.268\alpha – 1.268 = 0 \tag{13}$$ For the degree of dissociation, we get: $$\alpha =\dfrac{-b + \sqrt{b^2} -4ac}{2a} = \dfrac{-1.268 +\sqrt{1.268^2}+20.288}{8} \\= \dfrac{-1.268 +4679}{8} = 0.426 \tag{14}$$ Check your results: $$K_p = \dfrac{(P_{\ce{NO2}})^2}{P_{\ce{N2O4}}}=P\cdot \dfrac{( x_{\ce{NO2}})^2}{ x_{\ce{N2O4}}} = \mathrm{0.1315 \cdot \dfrac{(2\alpha)^2}{1-\alpha} =0.1315 \cdot \dfrac{0.852^2}{0.574}= 0.1663\ bar} \tag{15}$$

It looks like alpha $\alpha$ is the degree of dissociation. The way it is explained in your image is a little odd, so let me see if I can do a better job. What seems like it might be problematic for you is that the explanation you have been given skips some algebra along the way. Below, I am showing all of the algebra up until your points of confusion.

For your reaction: $\ce{N2O4 <=> 2NO2}$

In the first part of your question, we need to determine the equilibrium constant

$$K_p=\frac{P^2_{\ce{NO2}}}{P_{\ce{N2O4}}}$$

We know the total pressure, but we do not know the partial pressures of each species. Fortunately, thanks to Raoult's Law, we can substitute in mole fractions since $P_i =P \chi_i$.

$$K_p=\frac{P^2 \chi^2_{\ce{NO2}}}{P\chi_{\ce{N2O4}}}=P\frac{\chi^2_{\ce{NO2}}}{\chi_{\ce{N2O4}}}$$

We aren't given any number of moles, but let's say that initially there was some number of moles of $\ce{N2O4}$ before any dissociation occurred. We'll call that number $n_0$. We can write expressions for the number of moles of $\ce{N2O4}$ and $\ce{NO2}$ after dissociation using $n_0$ and $\alpha$. Since $\alpha\%$ of $\ce{N2O4}$ is dissociated, $(1-\alpha\%)$ remains undissociated:

$$n_{\ce{N2O4}}=n_0 (1-\alpha)$$

The moles of $\ce{NO2}$ are $n_0$ times $2\alpha$, since $\alpha\%$ of $\ce{N2O4}$ was converted into $\ce{NO2}$ and there are two $\ce{NO2}$ molecules for every $\ce{N2O4}$ molecule:

$$n_{\ce{NO2}} = 2n_0 \alpha$$

The total moles (need this for mole fraction) is

$$\sum{n}=n_{\ce{N2O4}} + n_{\ce{NO2}} = n_0 (1-\alpha) + 2n_0\alpha = n_0 (1-\alpha +2 \alpha) = n_0 (1+\alpha)$$

When we calculate the mole fractions of each species, the $n_0$ term cancels out, which is good since we do not know what its value is:

$$\chi_{\ce{N2O4}}=\frac{n_{\ce{N2O4}}}{\sum{n}}=\frac{n_0 (1-\alpha)}{n_0 (1+\alpha)}=\frac{1-\alpha}{1+\alpha}$$ $$\chi_{\ce{NO2}}=\frac{n_{\ce{NO2}}}{\sum{n}}=\frac{2n_0\alpha}{n_0 (1+\alpha)}=\frac{2\alpha}{1+\alpha}$$

Now you know where $1+\alpha$ came from. These values are plugged into the law of mass action for $K_p$ to determine the equilibrium constant.

In the second part of the question, you use the value of the equilibrium constant and the new pressure to determine a new value of $\alpha$. It all starts with the law of mass action and we manipulate some algebra from there. First the law of mass action using mole fractions:

$$K_p = P\frac{\chi^2_{\ce{NO2}}}{\chi_{\ce{N2O4}}}$$

Next, substitute in the expressions for mole fraction in terms of $\alpha$.

$$K_p = P\frac{\chi^2_{\ce{NO2}}}{\chi_{\ce{N2O4}}}=P\frac{\frac{(2\alpha)^2}{(1+\alpha)^2}}{\frac{1-\alpha}{1+\alpha}}$$

The term $1+\alpha$ appears in both the numerator and the denominator and can be canceled.

$$\require{cancel} K_p = P\frac{\frac{(2\alpha)^2}{\cancel{(1+\alpha)}(1+\alpha)}}{\frac{1-\alpha}{\cancel{(1+\alpha)}}}=P\frac{(2\alpha)^2}{(1-\alpha)1+\alpha}=P\frac{(2\alpha)^2}{1-\alpha^2}$$

Now we move $P$ over to the left side of the equation to separate the values we know ($K_p$ and $P$) from those we do not know ($\alpha$).

$$\frac{K_p}{P}=\frac{(2\alpha^2)}{1-\alpha^2}$$

Now you have something like your second equation that you are confused about. Perhaps there is a mistake in the original source?

• I still do not get it. Why haven't we squared 1 + alpha when you have written that xNO2 is squared? Shouldn't then the fraction go (2alpha/1+alpha) ^2 ? Why do we square only the numerator? – user33683 Aug 11 '16 at 13:52
• The equation is wrong, both terms should be squared as you noted. The bottom term should be 1-alpha^2 . – Cliff Stamp Jan 9 '17 at 1:22
• Good catch both of you. – Ben Norris Jan 9 '17 at 1:30


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# Subarray / Substring / Subsequence

Yao Yao on May 26, 2020

## Subsequence

Definition: Let $\langle x_n \rangle$ be a sequence in a set $S$. Let $\langle n_r \rangle$ be a strictly increasing sequence of indices in $\mathbb{N}$. Then the composition $\langle x_{n_r} \rangle$ is called a subsequence of $\langle x_n \rangle$.

• E.g., the prime numbers $\mathbb{P}$ are a subsequence of the natural numbers $\mathbb{N}$.

• E.g., $\langle A, C \rangle$ could be a subsequence of $\langle A, B, C \rangle$, but not a subarray

## Subarray

A subarray is a contiguous/consecutive subsequence of an array.

By contiguous/consecutive, 我觉得它的意思是 sequence of indices $\langle n_r \rangle$ is a sequence of consecutive integers $\langle m, m+1, m+2, \dots \rangle$

## Substring

A substring is exactly the same thing as a subarray but in the context of strings.


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PEER REVIEWED authorea.com/90610

# Are Galaxies Mostly Stars? Mass and Luminosity Determination of Spiral Galaxies and Stellar Groups

Abstract
In order to determine what spiral galaxies are composed of, we have to find their mass and their luminosity to produce a mass/luminosity ratio. This will help us determine what spiral galaxies are composed of because we can compare their mass/luminosity ratios to known stellar mass/luminosity ratios. By comparing these two different mass/luminosity ratios, we can determine if galaxies are composed mostly of stellar material. In this report, I will be analyzing 26 different spiral galaxies by finding their mass, their luminosity, and their mass/luminosity ratio. By using these techniques, I will show that only $$10\%$$ of the total galactic mass is made of stellar material and that $$90\%$$ of a galaxy is composed of non luminous “dark matter.”

# Introduction

A very important question in astronomy is if spiral galaxies are composed entirely of stellar material - stars. This question has puzzled astronomers for years and in this report, I will explain how to find the answer to this question. I will be finding the mass and luminosity of 26 different galaxies in order to find their mass/luminosity ratio. I will be using the Inital Mass Function to find the mass/luminosity ratio of stars and I will compare the two mass/luminosity values in order to find the percent of stellar mass in a galaxy. I will be using data from an astronomy Java program for the galaxy data and Guy Worthey’s Interpolation Medel (an Initial Mass Function program) for the stellar data.

This paper will be outlined as follows: Section 1: How to find the mass/luminosity relationship for Galaxies, Section 2: How to Determine a mass/luminosity relationship for Stars using the IMF, Section 3: Comparing the two different mass/luminosity relationships and what that means for Spiral Galaxies, and finally, Conclusions.

# Section 1: How to find the mass/luminosity Relationship for Galaxies

## Data and Analysis

The Java applet used for galaxy data provides the flux of the galaxy in $$Watt/ m^2$$, the velocity of the galaxy in $$km/s$$, and the X and Y position of the velocity data in arc seconds ("

It is important to understand that the only reason we can measure a doppler shift (and therefore a radial velocity) is because the galaxy has an inclination toward or away from Eath. The only reason doppler shifts happen is because the star are moving toward or away from Earth in their respective galactic orbit. For example, an inclination of 90 degrees is edge on, and an inclination of 0 degrees is face on, and any angle in between will describe the tilt from Earth. If the galaxy is face on, we can not measure a doppler shift, and therefore a radial velocity, because the stars are not moving toward or away from Earth, they are always the same distance away.


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# The sequence A is defined by the following relationship:

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The sequence A is defined by the following relationship:  [#permalink]

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07 Nov 2019, 02:13
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65% (hard)

Question Stats:

62% (02:34) correct 38% (03:02) wrong based on 61 sessions

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The sequence A is defined by the following relationship: $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$ for all integer values $$n >1$$. If $$A_1=1$$ , what is $$A_{15}-A_{13}$$ ?

A. 14
B. 29
C. 169
D. 196
E. 421

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Re: The sequence A is defined by the following relationship:  [#permalink]

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07 Nov 2019, 10:38
for the given function $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$
A1=1
A2=-3
A3= 6
A4=-10
A5=15
A6=-21
.
.
.
.
A13= 91 and A15= 120
A15-A13 = 29
IMO B

if there is any other short cut please share..

Bunuel wrote:
The sequence A is defined by the following relationship: $$A_n=A_{n-1}+(-1)^{n+1}(n)^2$$ for all integer values $$n >1$$. If $$A_1=1$$ , what is $$A_{15}-A_{13}$$ ?

A. 14
B. 29
C. 169
D. 196
E. 421

Are You Up For the Challenge: 700 Level Questions
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Joined: 12 Oct 2019
Posts: 41
Location: India
Concentration: Marketing, General Management
GMAT 1: 720 Q48 V41
GPA: 4
WE: Information Technology (Computer Software)
Re: The sequence A is defined by the following relationship:  [#permalink]

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08 Nov 2019, 05:55
A1=1
A2=-3
A3=6
A4=-10

Once we have found out till A4 we can see the pattern for the next term: add n to the absolute value of the previous and reverse the sign. For e.g. A5 = |A4| + 5 (with reversed sign).
So we can then quickly find out:

A5=15
A6=-21
A7=28
A8=-36
.
.
.
A13=91
A14=-105
A15=120

Hence A15-A13 = 29

B
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The sequence A is defined by the following relationship:  [#permalink]

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18 Dec 2019, 00:24
4
You should start from the ending, using the sequence formula.

A15 - A13 = A14 + 15^2 - A13 = A13 - 14^2 + 15^2 - A13 = (15-14) * (15+14) = 29
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Re: The sequence A is defined by the following relationship:  [#permalink]

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20 Dec 2019, 07:35
Har8 wrote:
You should start from the ending, using the sequence formula.

A15 - A13 = A14 + 15^2 - A13 = A13 - 14^2 + 15^2 - A13 = (15-14) * (15+14) = 29

Very elegant solution!
Thank you.

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Re: The sequence A is defined by the following relationship:  [#permalink]

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20 Dec 2019, 08:36
A1 = 1
A2 = -3
A3 = 6
A4= -10
A5=15
once we figure out a pattern it will simple and we Even Dont need to find out what A15 , A14 AND A13 is.

Difference between each term is mod n or |N| i.e. ||A2|-|A1|| =2 , ||A3|-|A2|| = 3, ||A4|-|A3|| =4
A15-A13=||A15|-|A14||+||A14|-|A13|| === 15+14 =29

So Answer is B, and we even didnt need to calculate all the numbers
Re: The sequence A is defined by the following relationship:   [#permalink] 20 Dec 2019, 08:36
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