text:
A rigid body rotates about a fixed axis with variable angular velocity equal to , at the time t, where $\alpha ,\beta$ are constants. The angle through which it rotates before its stops

1.  $\frac{{\alpha }^{2}}{2\beta }$

2.  $\frac{{\alpha }^{2}-{\beta }^{2}}{2\alpha }$

3.  $\frac{{\alpha }^{2}-{\beta }^{2}}{2\beta }$

4.

Concept Questions :-

Rotation motion : Introduction
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

For the uniform T shaped structure, with mass 3M, the moment of inertia about an axis normal to the plane and passing through O would be

1.  $\frac{2}{3}{\mathrm{MI}}^{2}$

2.  ${\mathrm{MI}}^{2}$

3.  $\frac{{\mathrm{MI}}^{2}}{3}$

4.  None of these

Concept Questions :-

Moment of inertia
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

An automobile moves on a road with a speed of 54 kmh${}^{-1}$. The radius of its wheel is 0.45 m and moment of inertia of the wheel about its axis of rotation is 3 kg m${}^{2}$. If the vehicle is brought to rest in 15s, the magnitude of average torque transmitted by its brakes to the wheel is

1. 8.58

2. 10.86

3. 2.86

4. 6.66

Concept Questions :-

Torque
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made 4 times, its angular momentum will become

1.  4L

2.  16L

3.

4.  2L

Concept Questions :-

Angular momentum
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Four particles of mass are placed at four corners of a square. What should be the value of ${\mathrm{m}}_{4}$ so that the center of mass of all the four particles are exactly at the center of the square?

1.  2m

2,  8m

3.  6m

4.  None of these

Concept Questions :-

Center of mass
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Angular momentum of a body is defined as the product of

1.  Mass and angular velocity

3.  Linear velocity and angular velocity

4.  Moment of inertia and angular velocity

Concept Questions :-

Angular momentum
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Two masses are connected to the ends of massless rope and allowed to move as shown in the figure. The acceleration of the centre of mass assuming pulley is massless and frictionless, is

1.

2.  0

3.

4.

Concept Questions :-

Center of mass
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The speed of a uniform spherical shell after rolling down an inclined plane of vertical height h from rest is

1.

2.

3.

4.

Concept Questions :-

Rolling motion
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Two identical balls marked 2 and 3. in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed v as shown in the figure. Assume the collision is elastic, then mark out the correct statement.

1.   Ball 2 comes to rest and ball 2 and 3 moves with speed each

2.  Ball I and 2 come to rest and ball 3 moves with speed v

3   Each ball moves with speed

4.  None of the above

Concept Questions :-

Linear momentum


text:
# \currentitle in memoir class header prints next section title

I have a weird problem with the memoir class.

I'm using it to typeset a book of short stories. I have the headers set up so that the page numbers are printed on the outer side. On the left-hand page, the book title is printed right-justified; on the right-hand page the title of the current story appears on the left. As far as I know, this is fairly usual. It looks like this:

Page number --- Book title | Story title --- Page number

The book title is inserted statically, i.e. not using any kind of command like \title. To get the story title I use \currenttitle thus:

\makeoddhead{headings}{\emph{\MakeUppercase{\currenttitle}}}{}{\thepage}

This all works fine except when a story finishes at the bottom of a right-hand page. Instead of printing that story's title in the header of that page, memoir uses the title of the story that begins overleaf!

I've not posted a minimal example, as the error obviously only occurs when you have the 'right' amount of text to fill up a few pages, but it is a reproducible error in the sense that it happens three times in this document with 30 stories in it.

Instead of a minimal example, here's the preamble:

\documentclass[postvopaper,twoside,10pt]{memoir}
\raggedbottom

\usepackage{fontspec} % Font selection for XeLaTeX; see fontspec.pdf for documentation
\defaultfontfeatures{Mapping=tex-text} % to support TeX conventions like \Emdash*''
\usepackage{xunicode} % Unicode support for LaTeX character names (accents, European chars, etc)
\usepackage{xltxtra} % Extra customizations for XeLaTeX
\usepackage{ellipsis}

\setmainfont{Lido STF} % set the main body font (\textrm)
\usepackage{amssymb,amsmath}
\setlength{\emergencystretch}{3em}  % prevent overfull lines
\setcounter{secnumdepth}{0}

\usepackage{graphicx}
\usepackage{covington}
\usepackage{enumitem}
\setlist[description{style=multiline,labelwidth=60pt,leftmargin=70pt%,itemindent=\dimexpr-20pt-\labelsep\relax
}

\usepackage{extdash}

% reduce size of footnote marker
\makeatletter
\renewcommand{\@makefnmark}{\hbox{\textsuperscript{\tiny{\@thefnmark}}}}
\makeatother

%%% PAGE LAYOUT

\setlrmarginsandblock{0.15\paperwidth}{*}{1} % Left and right margin
\setulmarginsandblock{0.2\paperwidth}{*}{1}  % Upper and lower margin
\sloppybottom
\checkandfixthelayout

%%-----------

\title{The Complete Annotated Reginald Stories}
\author{Saki}
\date{}

\makeevenhead{headings}{\thepage}{}{\emph{Complete Annotated Reginald Stories}}
\makeoddhead{headings}{\emph{\MakeUppercase{\currenttitle}}}{}{\thepage}
\pagestyle{headings}

• Please post a full minimal example, that makes it a lot easier to help you when we do not have to add anything to see the problem. IMO you're doing this wrong. You need to use \leftmark and \rightmark in order to access the latest sectonal title. These are usually specified using \makepsmarks, done right the \MakeUppercase will be build in as it isn't always that good as handling data stored in a macro. – daleif Apr 26 '16 at 10:01
• BTW: the kantlipsum package and its \kant macro is very handy to provide sample text – daleif Apr 26 '16 at 10:04
• I deliberately didn't give a minimal example, as the nature of the problem meant I would have had to fiddle about trying to get exactly the right amount of dummy text so that a section finished at the bottom of a page. (Otherwise the error won't occur.) Most lorem ipsum packages I know don't offer such a fine level of control. On the plus side, I changed \currenttitle to \rightmark and now it works, so thanks for your help! – Bruce Gaston Apr 27 '16 at 7:27
• Just see preparing an MWE as payment for peoples help. – daleif Apr 27 '16 at 7:49
• :-) Can you change your first comment to an answer so that I can mark the question as answered? – Bruce Gaston Apr 27 '16 at 14:01

## 1 Answer

Because of the asynchronous nature of the headers and footers, \currenttitle is not a good choice for the header. More traditionally \leftmark and \rightmark are used.

Also note that these marks are uppercase in memoir by default.

If interested you can have a look at the headings style code in the memoir sources, \makepsmarks and how it is used might be interesting.

There is also an article about memoir pagestyles in the PracTeX Journal, http://tug.org/pracjourn/2008-2/madsen/

format: plain


text:
# Show that an inverse of a bijective linear map is a linear map.

So I've got a bijection. It clearly has an inverse, but how exactly do I prove that the inverse is a linear map as well?

Suppose that the linear map $T:U\to V$ is a bijection. So $T$ has an inverse map $T^{-1}:V\to U$. Prove that $T^{-1}$ is a linear map.

Let $x,y\in V$. Since $T$ is a bijection, there exist $u,v\in U$ such that $T(u)=x,T(v)=y$. It follows that $$T^{-1}(x+y)=T^{-1}(T(u)+T(v))=T^{-1}(T(u+v))=u+v=T^{-1}(x)+T^{-1}(y)$$ and $$T^{-1}(kx)=T^{-1}(kT(u))=T^{-1}(T(ku))=ku=kT^{-1}(x)$$ for all scalar $k$.

Let $T:U\rightarrow V$ be given. We must prove for all $v_1,v_2\in V$ and $\alpha\in \mathbb F$ we have:

• $T^{-1}(u_1+u_2)=T^{-1}(u_1)+T^{-1}(u_2)$.
• $T^{-1}(\alpha u_1)=\alpha T^{-1}(u_1)$.

which is equivalent to:

• $u_1+u_2=T(T^{-1}(u_1)+T^{-1}(u_2))$.
• $\alpha u_1=T(\alpha T^{-1}(u_1))$.

you should be able to show this using the lineality of $T$.


text:
# deformation retraction of the complement

Let $X$ be a topological space and $V$ and $N$ are subspaces of $X$. It is known that if $V$ is homotopy equivalent to $N$ then $X-V$ need not be homotopy equivalent to $X-N$, the Alexander horned sphere is an example. In the context when $N$ deformation retracts onto $V$ it is still true that $X-V$ needs not deformation retracts onto $X-N$ as illustrated by the example of $X$ is the disk and $V$ is the equator and $N$ is the upper half disk.

Now in a paper the author and for $Qp(n)$ the quaternion projective space he says "Let $A^1$ be the complement of an open tubular neighborhood of $QP(n−1)$ in $QP(n)$" then he says "$A^1$ is a deformation retract of $QP(n) − QP(n − 1)$"

Is there any additional property that let this happen in this case.. thank you for the clarification!!

-
It might be more appropriate to remove the link to the paper, and just stick to the mathematical question. If it turns out there is an actual error in the paper, then the author could be contacted privately. –  Steven Gubkin Oct 15 '12 at 16:22
There are some situations of reasonable generality where what you ask for is true, but as stated in your first paragraph, it's false. For example, if $X$ is a 3-ball, $V$ and $N$ an embedded interval or a point respectively. The complements do not have to be homotopy-equivalent. Your latter comment about the paper, though, that's fine. It's part of the tubular neighbourhood theorem. –  Ryan Budney Oct 15 '12 at 16:28
What I mean to say is that statement in the paper is fine, and that's a fairly standard level of detail for that area. –  Ryan Budney Oct 15 '12 at 16:28


text:
Find all the points having a y-coordinate of -6 whose distance is from the point (1,2) is 17

jeew-m | Certified Educator

calendarEducator since 2012

starTop subjects are Math, Science, and Social Sciences

If we have two coordinates (a,b) and (c,d) the distance between the points R is given by;

`R = sqrt[(a-c)^2+(b-d)^2]`

For our question;

R = 17

a = 1

b = 2

c = ?

d = -6

`17 = sqrt[(1-c)^2+(2+6)^2]`

`17^2 = (1-c)^2+(8)^2`

`0 = c^2-2c-224`

Solution to the above quadratic equation is given by;

`c = ((-(-2)+-sqrt((-2)^2-4*1*(-224)))/(2*1))`

c = 16 or c = -14

So the x coordinates that satisfies the situation will be x = 16 and x = -14

check Approved by eNotes Editorial

Related Questions

Luca B. | Certified Educator

calendarEducator since 2011

starTop subjects are Math, Science, and Business

You should use distance formula such that:

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) `

Notice that the problem provides the both y coordinates `y_1 = 2` , `y_2 = -6` , one x coordinate, `x=1` , and the distance between the points, `d = 17` , hence, you should sbstitute these values in the formula of distance such that:

`17 = sqrt((x_2 - 1)^2 + (2 + 6)^2)`

`17 = sqrt((x_2 - 1)^2 + 64)`

You need to raise to square both sides such that:

`289 = (x_2 - 1)^2 + 64 =>(x_2 - 1)^2 = 289 - 64`

`(x_2 - 1)^2 = 225 => x_2 - 1 = +-sqrt(225) => x_2 - 1 = +-15`

`x_2 = 15 + 1 => x_2 = 16`

`x_2 = -15 + 1 => x_2 = -14`

Hence, evaluating the x coordinate of the points that follow the given conditions yields `(16,-6)`  and `(-14,-6).`

check Approved by eNotes Editorial


text:
# The description of abelian Lie groups

There is a problem in my problem sheet which asks me to describe all abelian connected Lie groups (moreover this is the first problem so it should be rather easy). I don't understand how this description should look. They mean description up to an isomorphism (of Lie groups), don't they?

I can list some abelian connected (real) Lie groups: $\mathbb{R}^n$, $\mathbb{C}_{\ne 0}$ (as a real group under multiplication), $S^1$ (i.e. $\{z\in\mathbb{C}: |z|=1\}$), also some different finite products. Could you help me to classify them?

• $\mathbb{R}_{\neq 0}$ is not connected, perhaps you meant $\mathbb{R}_{> 0}$ (which is isomorphic to $\mathbb{R}$, of course). – Jan Ladislav Dussek Mar 27 '14 at 20:48
• Oh, Really. Sorry. – Kolyan Mar 27 '14 at 20:53
• Hint: show that the exponential map is a homomorphism, where we consider the Lie algebra as an abelian Lie group under addition. – Nate Mar 27 '14 at 20:54

Nate's hint does the trick. Let $G$ be an abelian connected Lie group with Lie algebra $\mathfrak g$. The exponential map $\exp:\mathfrak g\to G$ is actually a homomorphism of abelian groups. The image is open in $G$, so $\exp$ is surjective because $G$ is connected. The fact that $\mathfrak g\to G$ is a local homeomorphism means that $\ker(\exp)$ is a discrete subgroup of $\mathfrak g$. It is known that such groups are of the form $\Lambda=\mathbf Z x_1+\cdots + \mathbf Z x_n$, for $x_1,\dots,x_n\in \mathfrak g$ linearly independent over $\mathbf R$. We can extend $x_1,\dots,x_n$ to a basis of $\mathfrak g$ to see that $$G \simeq (S^1)^r \times \mathbf R^s$$ In other words, every connected abelian Lie group is a product of affine space and a torus.

For example, $\mathbf C_{\ne 0} = \mathbf C^\times$ is the product $\mathbf R\times S^1$, via $(r,\theta)\mapsto r e^{i\theta}$.

• Hi @Daniel Miller do you have a reference for that? Could you precize what $r$ and $s$ are and if they are related? Thanks! – Hamurabi Jan 5 '16 at 0:14
• @Hamurabi no reference needed: I've included a complete proof. The integers $r$ and $s$ can be found by $r=\mathrm{rank} X_\ast(G)$ and $s=\dim(G)-r$. – Daniel Miller Jan 5 '16 at 17:43
• Thanks @Daniel Miller. Sorry for another question, but what is $rank X_{*}(G)$? – Hamurabi Jan 7 '16 at 13:27
• @DanielMiller: I want to cite the above result in a paper I'm writing. Can you direct me any references/paper where they prove the above fact ? – pikachuchameleon Jan 23 '16 at 17:54

If one knows the fundamental fact that a simply connected connected Lie group is completely determined by its Lie algebra, one can proceed as follows:

Let $G$ be an connected abelian Lie group of dimension $n$. The universal covering space $\tilde G$ is also a connected abelian Lie group of dimension $n$ which is, of course, simply connected; in particular, the Lie algebra of $\tilde G$ is of dimension $n$ and abelian. Since $\mathbb R^n$ is also a connected simply-connected Lie group with abelian Lie algebra of dimension $n$, we must have $\tilde G\cong\mathbb R^n$ as Lie groups. The point here is that there is exactly one^abelian Lie algebra of each dimension.

Now, the covering map $p:\tilde G\to G$ is a group homomorphism, so that $\ker p$ is a discrete subgroup of $\tilde G\cong\mathbb R^n$, so it is isomorphic to the subgroup generated by a linearly independent subset of $\mathbb R^n$. Using this it is easy to conclude what we want.

• Of course, the fundamental theorem I mentioned in the first paragraph is rather more difficult to prove that the result you want :-) – Mariano Suárez-Álvarez Mar 27 '14 at 22:20
• Can you direct me to any reference where it is proved that every connected abelian Lie group is isomorphic to product of affine spaces and torus ? – pikachuchameleon Jan 24 '16 at 4:55
• I'd say that this fact does not need a reference, as it is a basic part of Lie theory. Mine and Daniel's are two essentially complete proofs — you can reference this page, if you want! – Mariano Suárez-Álvarez Jan 24 '16 at 14:37
• Thanks. We work in areas that are not at all relevant to Lie group theory. that's why we wanted to cite the result in view of the target audience. – pikachuchameleon Jan 24 '16 at 15:34


text:
# Development¶

If you have not yet, please ‘install http://expfactory.readthedocs.org/en/latest/installation.html the expfactory python application.

## Contributing to code¶

We recommend that you work with developing experiment code using Github. If you aren’t familiar with Github, here is an introduction, and we provide more description below. This means that your general workflow will be as follows:

1. fork our experiments repo
1. clone the repository to your local machine
1. checkout a new branch for your update
1. when you are happy, commit changes locally, then to your fork
1. submit a pull request (PR) to our master branch to review the changes
1. keep in sync with our master

This will also be the general workflow for making any contributions to the battery, virtual machines, or python application.

### A. Fork our repos¶

When you browse to our repo, you will see a “Fork” button in the upper right (and the same is true for expfactory-surveys or expfactory-games):

Click it, and select your Github username to create a copy of the repository under your account name.

You can think of Github as a home in the cloud to store your code, along with a history of all changes. This means that many people can collaboratively work on the same code and have a way to talk about changes, report issues, and merge it all together in the end. The way that Github works is based on having this “remote” version, along with a “local” version on your computer. The code base is generally called a “repository” (repo for short), and the way it is organized is based on branches. There is usually a default branch that is the “working” and “up to date” version of the code, and this is usually called “master.” When you fork a repo, you should generally keep your version of “master” synced with the main (upstream) repository master. This is because we will use this branch as a template for all new branches. You can imagine if you are working on two features, you would want for each one to have a separate branch in your repo. If you use your master branch to work on the first feature, then you have no way of easily creating a fresh branch that is in sync with the upstream repo master that you forked. When someone talks about “getting code from” a repo, they usually will use the term “pull,” and this is why when you make changes and ask another repo to accept (pull) your changes, it is called a “pull request.” Sending code to the cloud repo will use the term “push.” Rest assured that these terms and development practices will become second nature when you get into the groove of things. We will provide detailed instructions when possible, and please tell us if something is not clear.

### B. Clone the repository to your local machine¶

After you fork the repo, you have created a version in the cloud associated with your account. But to work with it, you need to “clone” it to your local machine. You can do this by way of:

git clone https://github.com/[your-username]/expfactory-experiments

Note that if you use ssh (instructions for setup are here) you should clone like this:

git clone git@github.com:[your-username]/expfactory-experiments.git

A repository is “connected” to Github via a simple config text file. If you look at this file, you can understand quickly how simple it is. For example, let’s say we just cloned the experiments repo:

cd expfactory-experiments

There is a hidden folder called ”.git” with a config file in it. Generally you should not manually edit files in this folder, but the config is pretty easy to understand, and easy to edit to change the names of your repos or add other repos to push and pull to. Let’s take a look at a standard config file:

vim .git/config

[core]
repositoryformatversion = 0
filemode = true
bare = false
[remote "origin"]
url = git@github.com:vsoch/expfactory-experiments.git
[branch "master"]
remote = origin

We want to make a quick change to this file. The rationale for this change is that many people might be working on expfactory experiments, and our version of “master” can quickly fall behind the expfactory master. With this in mind, we want to be able to easily “pull” from the expfactory master, which we will call “upstream.” Here is my config file for the expfactory-python. Since I want to work with the “upstream” (main expfactory Organization repo) along with my version (associated with username vsoch) you will notice that I have added a few lines to specify an “upstream” remote:

[core]
repositoryformatversion = 0
filemode = true
bare = false
[remote "upstream"]
url = git@github.com:expfactory/expfactory-experiments.git
[remote "origin"]
url = git@github.com:vsoch/expfactory-experiments.git
[branch "master"]
remote = origin

This means that, whenever I want to checkout my master to create a new branch from, or when either my PR or someone else’s PR has been merged into the expfactory master, I should pull from upstream and push to my master:

git pull upstream master

It will open a text file that is asking for you to commit a merge. Save this file to do so. Then push to your master:

git push origin master

If you get errors about merge conflicts, this means that something was out of order, and you need to open up files that have conflicts to resolve the conflicts, and then commit. If you only use your master as a template to checkout new branches from, you should not run into this problem.

For the above example, you will also notice that the format of the URLs follows the SSH standard, because that is how I cloned it, and how it is setup on my computer. If you get errors about authentication, you likely have the wrong format specified in your config. A https url would look something like:

[core]
repositoryformatversion = 0
filemode = true
bare = false
[remote "origin"]
url = https://github.com/vsoch/expfactory-experiments.git
[branch "master"]
remote = origin

It’s pretty common to clone with HTTPS (copy pasting the url for a repo), and then edit the config to change to SSH to push and pull. You can define as many remotes as you like in this file so you can easily pull from your colleagues repos if you want to test what they are working on.

### C. checkout a new branch for your update¶

You’ve now cloned the repository to your local machine, and you would want to check out a new branch to make an update. First, see what branch you are on:

git branch
* master

Then checkout a new branch, it’s a good standard to give it a tag to describe what you are doing (fix/update/enh) and then a specific name. For example:

git checkout -b update/add_my_experiment

You will then be switched to your new branch

git branch
master

Once the branch is created, it should be standard practice for you to first see what branch you are on before starting work for the day. If you need to switch, you don’t need the “-b” argument:

git checkout master

### D. commit changes¶

It’s good practice to commit changes locally when you are happy, adding a message to provide details about what you’ve changed. You may first want to compare your recent work to what is on Github, and you can do this with:

git status

It will show you changed, deleted, and added files. You can then “commit” these changes to your local repo, which basically means writing them into some local record in the .git folder to prepare for pushing to the remote repo:

git commit -a

is read as “git commit all” and it will open up a text editor to show you a summary of the changes. It is expected with each commit that you describe what you have done in a message. You can either uncomment lines in the file (remove the “#”) or write a message right at the top. Saving the file will commit the changes locally.

Finally, you can push to your local branch. The format is like:

git push [remote] [branch]

where [remote] and [branch] correspond to the name of the remote and branch (in the .git/config) which means that for our example we might do:

git push origin update/add_my_experiment

### E. submit a pull request (PR) to our master branch¶

Once you have made a change, and commit the change to your remote (cloud) repo, you would want to submit this change to us to consider merging into the expfactory master branch. It’s easiest to do this with the online interface. You should go to your repo, and find the “Pull Request” button:

You will then want to select merging your base/branch into the expfactory/master branch. Please tell us in the comments what you have changed or added, and then submit the PR. We will be able to review your changes and give you feedback.

### F. keep in sync with our master¶

As we detailed above, remember that many people might be submitting PRs to work on the same code base, which means that your master branch can fall behind. Whether you are updating your master after your PR (or someone else’s) was merged, this should be the first thing you do before checkout of a new branch:

git checkout master
git pull upstream master
git push origin master

Now that you are a development Github pro, you might want more details about the format of a new experiment.

Whether you want to contribute a survey, an experiment, or a game, the basic steps and structure of what you create will be the same. Each of surveys, experiments, and games has a repository under  the expfactory github organization <http://www.github.com/expfactory>_ and each repository is a collection of folders, with one paradigm for folder. You can store folders on your server or local machine, or just have our software grab the latest version directly from the repositories. The commonality between folders is that they all have a configuration file, the config.json, with a set of standard fields that are defined to allow the Experiment Factory Python Software to work with paradigms. A few notes about the config.json:

• You do not need to define fields in the config.json that are not required. Use expfactory –validate to see if you did it right.
• the folder name must correspond with the “exp_id” variable in the config.json
• experiment, survey, and game folder names should be all lowercase, no hyphens (-), or spaces.

### config.json¶

A data structure that specifies the following:

• name: [required] the full name of the experiment, best is to use the name of the publication it is associated with.
• exp_id: [required] the experiment id (unique identifier) for the experiment, typically the folder name, all lowercase with no special characters.
• cognitive_atlas_task_id: [optional] the identifier for the experiment defined in the cognitive atlas
• contributors: a list of contributors to the task code base.
• reference: url(s) to referenced papers to develop the task. This field is to be removed, and the reference or DOI should be stored in the CognitiveAtlas.
• experiment_variables: should be a list of dictionaries to specify one or more variables to be available for use to measure performance, allocate bonus, or receive credit. The fields of this variable include “name” “type” “label” “range” and “description.” The “label” field will determine if the Experiment Factory docker virtual machine will parse the variable as being available to use for a reward (eg, label == “reward”) or for allocation of credit (eg, label == “credit”).
• notes: any notes about the implementation, etc.
• publish: [required] either “True” or “False” to determine if the experiment should be revealed to the user of the expfactory-python application.
• deployment_variables: a dictionary of customizations for the javascript template. For example, jspsych has a jspsych_init object that you may want to customize.
• run: [required] entry javascript and css files for the experiment. Paths here should all be relative to the experiment folder, and will be used to embed the experiments in different contexts. For example, the following files in run in the folder multisource:
"run": [
"experiment.js",
"style.css",
"static/js/jspsych/plugins/plugin.js"
],

will produce the following in a rendered template:

<link rel='stylesheet' type='text/css' href='static/experiments/multisource/style.css'>

<script src='static/js/jspsych/plugins/plugin.js'></script>
<script src='static/experiments/multisource/experiment.js'></script>

Note that the full path is a file served in our expfactory-battery (a plugin common to many experiments), and the local paths are files in the multisource experiment folder.

An example of a config.json data structure is as follows:

[
{
"name": "Model-Based Influences on Humans' Choices and Striatal Prediction Errors",
"exp_id": "two_stage_decision",
"template":"jspsych",
"contributors": [
"Ian Eisenberg",
"Zeynep Enkavi",
"Patrick Fisher",
"Vanessa Sochat",
"Russell Poldrack"
],
"run": [
"experiment.js",
"style.css",
"plugin.js"
],
"reference": "http://www.sciencedirect.com/science/article/pii/S0896627311001255",
"notes": "Condition = ordered stims in stage 1 and stage 2 (so [0, 1] or [1, 0] for stage 1 and [2, 3], [4, 5] etc. for stage 2 and FB for the FB condition (1 for reward, 0 for no reward)",
"publish": "True"
}
]

#### experiment_variables¶

Here are examples of different kinds of experiment variables. If you do not have any, you don’t need to define this field, or you can define like this:

"experiment_variables":"",

A boolean variable that is to be used to calculate bonus for a task

"experiment_variables": [{
"name":"passed_check",
"type":"bonus",
"datatype":"boolean"
"description":"JavaScript boolean to indicate the participant passed the check."
}]

A numeric variable (both int and float are stored as float) to be used to assess if credit should be given (or not)

"experiment_variables": [{
"name":"number_correct",
"type":"credit",
"datatype":"numeric",
"range":[0,100],
"description":"the total number of correct choices."
}]

A string variable that will be included as a model (we will be including other ways to explore results, not implemented for now) but not intended for allocation of credit / rejection, or bonus:

"experiment_variables": [{
"name":"quality_label",
"datatype":"string",
"range":["low","average","good","very good"],
"description":"The quality of the responses."
}]

#### deployment_variables¶

A deployment variable is specific to the javascript template / architecture that the experiment is using. We only support jspsych, and so you can only specify “jspsych_init.” You do not need to define this variable if you don’t have any customizations, but here is how to define an empty variable:

"deployment_variables":""

Specify a field in jspsych_init

"deployment_variables":{"jspsych_init":
{
}
}

#### run¶

A list of javascript and css files that are essential for the experiment to run, specified in load_experiments.js (see details above). Typically, an experiment will have an experiment.js file and a style.css. For jspsych files that are included with the expfactory-battery/js folder, specify the complete path to the file relative to the static folder. For example:

static/js/jspsych/plugins/jspsych-call-function.js

Any files with full paths specified as the above will be checked for existance within the expfactory-battery folder. If found, the file will be linked successfully. If not found, the file will be looked for in the experiment folder. If the file does not exist in either place, an error will trigger upon generation of the battery.

## Contributing to experiments¶

An experiment is just a folder with files that are expected to be a certain way. The “core” of an experiment is:

• config.json: a file with a bunch of information about an experiment, meta-data
• experiment.js: the main javascript file to run the experiment
• style.css: (optional) custom styling

A recommended strategy for developing a new experiment is to find an experiment similar to the one you want to make, copy the folder, and edit it. We recommend using JsPsych for tutorials, help, and examples, as the documentation is really great. We also provide an standard reaction time (commented) empty template for you to download, and in the future will provide a dynamic web interface for generating new templates. When you submit a PR to the expfactory-experiments repo, the experiment will be tested with continuous integration, and before doing this, we have provided a simple command line tool that can be used to validate the basics about the config.json and experiment folder.

cd my_new_experiment
expfactory --preview   # preview / run the experiment in the browser within the PWD
expfactory --validate  # will validate config.json and experiment structure
expfactory --test      # will run test robot we run on continuous integreation

### Summary of Best Practices¶

• An experiment must minimally have an experiment.js and valid config.json file
• We use jspsych plugins for most experiments, and most are included with the battery repo, meaning you don’t need to include them with your local folder, but rather specify their path in the “run” variable of your config.json (see below).
• you can include any images/sounds supplementary files in your experiment folder, it will be included
• these supplementary files specified in experiment.js should have paths relative to the battery experiment base directory, static/experiments/[exp_id]/images/hello.png
• supplementary files specified in style.css should be relative to the experiment folder.

Files hard coded into the experiment.js should have a path with the following format:

/static/experiments/[folder-name]/images/

where folder-name is replaced with the name of the experiment folder, and any subdirectories to that (e.g., “images” should exist in the experiment directory. For example, to link a sound file in an experiment folder, tone-monitoring:

practice_stims = [{sound: '/static/experiments/tone_monitoring/sounds/880Hz_-6dBFS_.5s.mp3',
data: {exp_id: 'tone_monitoring', trial_id: 'high', condition: 'practice'}},
{sound: '/static/experiments/tone_monitoring/sounds/440Hz_-6dBFS_.5s.mp3',
data: {exp_id: 'tone_monitoring', trial_id: 'medium', condition: 'practice'}},
{sound: '/static/experiments/tone_monitoring/sounds/220Hz_-6dBFS_.5s.mp3',
data: {exp_id: 'tone_monitoring', trial_id: 'low', condition: 'practice'}}
]

These files would be in the tone-monitoring experiment folder as:

tone_monitoring/
sounds/
880Hz_-6dBFS_.5s.mp3
440Hz_-6dBFS_.5s.mp3
220Hz_-6dBFS_.5s.mp3

as the entire thing will be included in the experiment’s folder (under /static/experiments/[folder-name]), with the same structure. You are free to include any necessary static files in your experiment, and can name subfolders in your experiment folder however you like. Most of these files do not need to be specified in the “run” variable of the config.json. These specified files should be those js and css that will be embedded in the dynamically produced experiment html so that the experiment functions. If you find that your experiment is not running, likely you can inspect the console and see that you are missing a file. When validation of an experiment occurs upon battery generation, all files specified in this “run” variable will be checked for existence, and an error output if not found.

### experiment.js¶

This is the main javascript file to run the experiment. This file should include set up of the JsPsych experiment, and the requirement is that the resulting array of blocks be named {{exp_id}}_experiment (for example, if the folder is called “local_global” the array that finishes the file, onto which all blocks are pushed, is called “local_global_experiment.” When defining your blocks, in the “data” variable you must include “exp_id” to also specify this unique identifier (e.g., local global). Not including the unique ID with the data will trigger an error during continuous integration testing, and will possibly mean that you could have data that cannot be linked back to a task.

Paths to images, sounds, and other files referenced in this file will be expected to follow the same pattern as above, e.g.: /static/experiments/[folder-name]/images/filename.png (required).

### Supplementary files¶

You might want a folder of images, sounds, or other, to be included with your experiment. You are allowed to include, and specify these files as needed in the style.css or experiment.js. Important** if you specify an image/other in the style sheet, the path should be relative to the css file (the experiment folder). If you specify an image or file in your experiment.js file, the path should be relative to the battery base folder (e.g., /static/experiments/[folder-name]/images/.

### style.css¶

Is the main style file for the experiment, which will be copied into the battery style folder and linked appropriately. Images that are defined in this file should have paths relative to the images folder. (required).

## Contributing to surveys¶

A survey is the easiest of our paradigms to contribute to, as an entire survey is just a tab delimited text file paired with a config.json in a folder in expfactory-surveys. In the config.json, “template” should be “survey”. The easiest way to understand the tab delimited file is to look at an example.

You will notice the following columns in the header, which is the first row of the file:

• question_type: can be one of textfield, numeric (a numeric text field), radio, checkbox, or instruction. These are standard form elements, and will render in the Google Material Design Lite style.
• question_text: is the text content of the question, e.g., How do you feel when you wake up in the morning?
• required: is a boolean (0 or 1) to indicate if the participant is required to answer the question (1) or not (0) before moving on in the survey.
• page_number: determines the page that the question will be rendered on. If you look at an example survey you will notice that questions are separated by Next / Previous tabs, and the final page has a Finish button. It was important for us to give control over pagination to preserve how some “old school” questionnaires were presented to participants.
• option_text: For radio and checkboxes, you are asking the user to select from one or more options. These should be the text portion (what the user sees on the screen), and separated by commas (e.g, Yes,No,Sometimes. Note: these fields are not required for instructions or textbox types, and can be left as empty tabs.
• option_values: Also for radio and checkboxes, these are the data values that correspond to the text. For example, the option_text Yes,No may correspond to 1,0. Again, this field is typically blank for instructions or textbox types.

## Contributing to games¶

Games are under development, and currently we are using “phaser” as a first template. As with surveys and experiments, you are required to have a config.json, and the “template” variable should be defined as “phaser”. Standards are under development, and an updated list can be found at expfactory-games repo. Currently, the following is required:

• the main game file should be called Run.js
• the boolean variable “finished” included with every trial (0 to continue/1 to finish)
• the game should have an inputData function that updates a data object when appropriate.

While we further develop the standard, please see a finished game (code/live)as an example.

## Testing¶

It makes most sense to work directly from a folder in the expfactory-experiments repo that you have cloned. This method will work if you have an internet connection, as the expfactory executable will quickly plug your experiment into a battery, and open up the page in your browser. To do this, you can cd into your experiment folder, and use the –run command. This command can be used to run or preview a single experiment locally:

cd simple_experiment
expfactory --run

You can also specify the folder as an argument:

expfactory --run --folder /home/vanessa/Desktop/simple_rt

You can also specify a port:

expfactory --run --port=8088

Your browser will open to show the experiment. You can press Control+C to shut down the server.

As stated previously, you should validate your config.json, folder structure and files, by running:

cd simple_experiment
expfactory --validate

This function also works to specify a folder

expfactory --validate --folder /home/vanessa/Desktop/simple_rt

You can use the experiment robot to test your experiment locally. The same functions are used that will be run for continuous integration, and it is a good idea to make sure that no errors are output before submitting a PR.

cd simple_experiment
expfactory --test

or to specify a folder

expfactory --test --folder /home/vanessa/Desktop/simple_rt

Finally, if you add a new experiment, you will need to add a line to test it in the circle.yml. You can test the circle.yml before pushing as follows:

from expfactory.tests import validate_circle_yml
validate_circle_yml('expfactory-experiments')

Continuous integration is a term from software development that basically means we test as we change and modify our code - in this case “code” is referring to the different experiments. This means that when you submit a pull request (PR) to the expfactory-experiments repo, along with local testing that you might do, we also test the code on a continuous integration server called CircleCI. You will see a link to your PR from Github as soon as the PR is submit. Your contribution will be assessed based on the following:

• validation tests passing, meaning that your config.json and experiment folder are formatted and named properly
• jshint: we test the static code with jshint. If there are issues for your experiment, tests will not pass.
• robot tests: we have developed a robot that can be run locally or with continuous integration. The robot will click through the task, make random selections, and trigger an error if a 404 is found.
• experiment running: If you click on “Artifacts” tab at the top when the testing finishes, you will see a hierarchy of the machine, and you can go to ubuntu/expfactory-experiments/web/index.html to open up a browser and see the dynamically generated updated experiment set. If you click on “browse our experimental paradigms” from the box in the top right corner, and you should be able to find your experiment in the table and preview it. Note that the first tree view of the experiments points to expfactory.github.io. You should open your developer console, as you would on your local machine, and run through the experiment both looking for errors (that might have been detected by the robot) and seeing that things run as expected.

Currently, we only test changes between the last successful build and your contribution, meaning experiment folders with changed files. Since the entire battery would take upwards of 10 hours, we recommend you submit PRs limited to a few experiments, otherwise the running will take a very long time.

If you want to work offline, or simply want to develop an experiment using psiturk, then you will want to take the following approach:

• use the expfactory tool to generate a battery
• move the battery folder from your tmp directory to where you want it
• copy experiment folders / create new folders into the battery “/static/experiments” folder
• test and debug using psiturk (instructions not provided here)
• move the folder back to your expfactory-experiments repo, commit changes, and push as normal.

### Getting Help¶

Please submit an issue to our code base, or email someone in the lab, and we will do our best to help. Please remember that we are a small group of (mostly) graduate students, and will respond as promptly as we can.

### Debugging¶

If you see a white screen, it usually means there is a JavaScript error. While we can’t provide details here for how to debug everything, generally if you right click –> Inspect Element and click the “console” tab you will see red text that indicates some JavaScript error. Questions to ask:

• Did you specify all required jspsych scripts in your “run” variable? A script that is not specified will not be included in the page, and you will likely see a message like this:
• Is the jspsych script included with the battery? If you specify a path in the run variable in config.json and it’s not found, it’s likely not included in the battery repo, and you can look to check. If you are missing a script and would like one added, please submit a PR to the repo and it will be done, and this will fix your error.
• Is your browser caching an old script? You might make a change, but then the error persists, and this is because the browser caches style and js files by default. You can disable this in the settings, so it won’t cache when the development console is open:

or you can use Incognito mode (Control + Shift + N).

• Do you have a syntax error or a missing variable?
• What is the scope of your variable? If you reference a variable inside a function, it will not be available outside of that function. This is called scope.

Debugging JavaScript is hard and annoying. We chose to use jspsych rather arbitrary, and please let us know if you want support for other libraries (meaning we provide them in the battery repo). May the force be with you.

## Contributing to this documentation¶

The documentation lives in the “doc” folder. Specifically, this is sphinx documentation that gets built automatically. The “build” folder contains the output that we serve on github pages, and this works by linking the index.html in the repo base to doc/build/html. The “source” folder contains files that you will want to edit.

You will need to install sphinx to work with these files

sudo pip install sphinx

And familiarize yourself with the restructured text (rst) documentation syntax.

The basic infrastructure is set up, so you should be able to edit the places that you need, and if you need help with something more advanced (and you can’t figure it out) contact someone else in the Poldracklab or just submit an issue <https://github.com/expfactory/expfactory-python/issues>_.

### Basic workflow¶

1. Edit a file
2. Enter the documentation base folder
cd doc
make html

Note that you should READ the error messages in the console when you build - it will tell you if you forgot to include files, or have any other syntax errors. Then:

cd build/html
python -m SimpleHTTPServer -9999

This will start a local web server using python at localhost:9999.

1. Open your browser to localhost:9999 to preview


text:
# zbMATH — the first resource for mathematics

## Włodarczyk, Kazimierz

Compute Distance To:
 Author ID: wlodarczyk.kazimierz Published as: Włodarczyk, Kazimierz; Włodarczyk, K.; Wlodarczyk, Kazimierz; Włodarczyk, Kazimier; Wlodarczyk, K.
 Documents Indexed: 78 Publications since 1977
all top 5

#### Co-Authors

 44 single-authored 24 Plebaniak, Robert 7 Klim, Dorota 4 Obczyński, Cezary 2 Banach, Artur 2 Szałowska, Alina 1 Doliński, Mariusz 1 Gonicka, Joanna 1 Gontarek, E. 1 Kowalczyk, Robert 1 Wardowski, Dariusz
all top 5

#### Serials

 13 Fixed Point Theory and Applications 10 Journal of Mathematical Analysis and Applications 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Annales Polonici Mathematici 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Demonstratio Mathematica 4 Atti del Seminario Matematico e Fisico dell’Università di Modena 3 Monatshefte für Mathematik 3 Proceedings of the American Mathematical Society 3 Abstract and Applied Analysis 2 Indagationes Mathematicae 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Annales Societatis Mathematicae Polonae. Seria I. Commentationes Mathematicae 2 Complex Variables. Theory and Application 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Advances in Mathematics 1 Topology and its Applications 1 Applied Mathematics Letters 1 Glasnik Matematički. Serija III 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
all top 5

#### Fields

 37 Operator theory (47-XX) 34 Functional analysis (46-XX) 28 General topology (54-XX) 17 Functions of a complex variable (30-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Global analysis, analysis on manifolds (58-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX)

#### Citations contained in zbMATH Open

45 Publications have been cited 435 times in 172 Documents Cited by Year
Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces. Zbl 1185.54020
Włodarczyk, Kazimierz; Plebaniak, Raobert; Obczyński, Cezary
2010
Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Zbl 1182.54024
Włodarczyk, Kazimierz; Plebaniak, Robert; Banach, Artur
2009
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances. Zbl 1201.54039
Włodarczyk, Kazimierz; Plebaniak, Robert
2010
Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions. Zbl 1203.54051
Włodarczyk, Kazimierz; Plebaniak, Robert; Doliński, Mariusz
2009
Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces” [Nonlinear Anal. (2008), doi: 10.1016/j.na.2008.04.037]. Zbl 1171.54311
Włodarczyk, Kazimierz; Plebaniak, Robert; Banach, Artur
2009
Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces. Zbl 1110.54025
Włodarczyk, K.; Klim, D.; Plebaniak, R.
2007
Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces. Zbl 1193.37101
Włodarczyk, Kazimierz; Plebaniak, Robert
2010
Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances. Zbl 1233.54019
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces. Zbl 1148.54021
Włodarczyk, Kazimierz; Plebaniak, Robert
2008
Kannan-type contractions and fixed points in uniform spaces. Zbl 1311.47075
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
Contractions of Banach, Tarafdar, Meir-Keeler, Ćirić-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances. Zbl 1304.47067
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
A fixed point theorem of Subrahmanyam type in uniform spaces with generalized pseudodistances. Zbl 1206.54068
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces. Zbl 1124.54005
Włodarczyk, Kazimierz; Plebaniak, Robert; Obczyński, Cezary
2007
Leader type contractions, periodic and fixed points and new completivity in quasi-gauge spaces with generalized quasi-pseudodistances. Zbl 1258.47075
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Julia’s lemma and Wolff’s theorem for $$J^ *$$-algebras. Zbl 0621.46041
Włodarczyk, Kazimierz
1987
Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems. Zbl 1213.81161
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fixed points. Zbl 1280.54012
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Zbl 1295.41039
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized pseudodistances. Zbl 06235304
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces. Zbl 1202.54016
Włodarczyk, Kazimierz; Plebaniak, Robert; Obczyński, Cezary
2007
Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces. Zbl 1095.54019
Włodarczyk, K.; Obczyński, C.; Wardowski, D.
2006
Quasi-triangular spaces, Pompeiu-Hausdorff quasi-distances, and periodic and fixed point theorems of Banach and Nadler types. Zbl 1433.54033
Włodarczyk, Kazimierz
2015
New completeness and periodic points of discontinuous contractions of Banach-type in quasi-gauge spaces without Hausdorff property. Zbl 1295.54095
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
Equilibria and fixed points of set-valued maps with nonconvex and noncompact domains and ranges. Zbl 1108.47047
Włodarczyk, K.; Klim, D.
2006
Quasi-asymptotic contractions, set-valued dynamical systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces. (Quasi-asymptotic contractions, set-valued dynamic systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces.) Zbl 1160.54011
Włodarczyk, Kazimierz; Plebaniak, Robert
2009
Iterations of holomorphic maps of infinite dimensional homogeneous domains. Zbl 0554.46019
Włodarczyk, Kazimierz
1985
Studies of iterations of holomorphic maps in $$J^*$$-algebras and complex Hilbert spaces. Zbl 0595.47046
Włodarczyk, Kazimierz
1986
Generalized contractions of Meir-Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces. Zbl 1158.54005
Włodarczyk, Kazimierz; Plebaniak, Robert
2008
Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces. Zbl 1388.54030
Włodarczyk, Kazimierz
2014
The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces. Zbl 0817.46048
Włodarczyk, Kazimierz
1993
Fixed-point and coincidence theorems for set-valued maps with nonconvex or noncompact domains in topological vector spaces. Zbl 1020.47050
Włodarczyk, Kazimierz; Klim, Dorota
2003
Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces. Zbl 1350.54021
Włodarczyk, Kazimierz; Plebaniak, Robert
2015
Random iterations of holomorphic maps in complex Banach spaces. Zbl 0958.46026
Wlodarczyk, K.; Klim, D.; Gontarek, E.
2000
On holomorphic maps in Banach spaces and $$J^*$$-algebras. Zbl 0595.46048
Włodarczyk, Kazimierz
1985
Periodic and fixed points of the Leader-type contractions in quasi-triangular spaces. Zbl 1367.54030
Włodarczyk, Kazimierz
2016
Fuzzy quasi-triangular spaces, fuzzy sets of Pompeiu-Hausdorff type, and another extensions of Banach and Nadler theorems. Zbl 1342.54038
Włodarczyk, Kazimierz
2016
Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains. Zbl 0802.46060
Włodarczyk, Kazimierz
1994
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of $$C^*$$-algebras. Zbl 0827.47030
Włodarczyk, Kazimierz
1994
Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces. Zbl 0933.46040
Włodarczyk, Kazimierz; Gonicka, Joanna
1999
Angular derivatives of holomorphic maps in infinite dimensions. Zbl 0881.32004
Włodarczyk, Kazimierz; Szałowska, Alina
1996
Pick-Julia theorems for holomorphic maps in $$J^ *$$-algebras and Hilbert spaces. Zbl 0612.46044
Włodarczyk, Kazimierz
1986
New extension of the Banach contraction principle to locally convex spaces and applications. Zbl 0654.47038
Włodarczyk, Kazimierz
1988
Approximative fixed points of compact holomorphic maps in complex Banach spaces. Zbl 0667.47033
Włodarczyk, Kazimierz
1988
Some properties of analytic maps of operators in J*-algebras. Zbl 0521.46046
Wlodarczyk, Kazimierz
1983
On the existence and uniqueness of fixed points for holomorphic maps in complex Banach spaces. Zbl 0744.47050
Włodarczyk, Kazimierz
1991
Periodic and fixed points of the Leader-type contractions in quasi-triangular spaces. Zbl 1367.54030
Włodarczyk, Kazimierz
2016
Fuzzy quasi-triangular spaces, fuzzy sets of Pompeiu-Hausdorff type, and another extensions of Banach and Nadler theorems. Zbl 1342.54038
Włodarczyk, Kazimierz
2016
Quasi-triangular spaces, Pompeiu-Hausdorff quasi-distances, and periodic and fixed point theorems of Banach and Nadler types. Zbl 1433.54033
Włodarczyk, Kazimierz
2015
Dynamic processes, fixed points, endpoints, asymmetric structures, and investigations related to Caristi, Nadler, and Banach in uniform spaces. Zbl 1350.54021
Włodarczyk, Kazimierz; Plebaniak, Robert
2015
Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces. Zbl 1388.54030
Włodarczyk, Kazimierz
2014
Contractions of Banach, Tarafdar, Meir-Keeler, Ćirić-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances. Zbl 1304.47067
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Zbl 1295.41039
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
New completeness and periodic points of discontinuous contractions of Banach-type in quasi-gauge spaces without Hausdorff property. Zbl 1295.54095
Włodarczyk, Kazimierz; Plebaniak, Robert
2013
Contractivity of leader type and fixed points in uniform spaces with generalized pseudodistances. Zbl 1233.54019
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Leader type contractions, periodic and fixed points and new completivity in quasi-gauge spaces with generalized quasi-pseudodistances. Zbl 1258.47075
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Generalized uniform spaces, uniformly locally contractive set-valued dynamic systems and fixed points. Zbl 1280.54012
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Fixed points and endpoints of contractive set-valued maps in cone uniform spaces with generalized pseudodistances. Zbl 06235304
Włodarczyk, Kazimierz; Plebaniak, Robert
2012
Kannan-type contractions and fixed points in uniform spaces. Zbl 1311.47075
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
A fixed point theorem of Subrahmanyam type in uniform spaces with generalized pseudodistances. Zbl 1206.54068
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems. Zbl 1213.81161
Włodarczyk, Kazimierz; Plebaniak, Robert
2011
Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces. Zbl 1185.54020
Włodarczyk, Kazimierz; Plebaniak, Raobert; Obczyński, Cezary
2010
Maximality principle and general results of Ekeland and Caristi types without lower semicontinuity assumptions in cone uniform spaces with generalized pseudodistances. Zbl 1201.54039
Włodarczyk, Kazimierz; Plebaniak, Robert
2010
Periodic point, endpoint, and convergence theorems for dissipative set-valued dynamic systems with generalized pseudodistances in cone uniform and uniform spaces. Zbl 1193.37101
Włodarczyk, Kazimierz; Plebaniak, Robert
2010
Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Zbl 1182.54024
Włodarczyk, Kazimierz; Plebaniak, Robert; Banach, Artur
2009
Cone uniform, cone locally convex and cone metric spaces, endpoints, set-valued dynamic systems and quasi-asymptotic contractions. Zbl 1203.54051
Włodarczyk, Kazimierz; Plebaniak, Robert; Doliński, Mariusz
2009
Erratum to: “Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces” [Nonlinear Anal. (2008), doi: 10.1016/j.na.2008.04.037]. Zbl 1171.54311
Włodarczyk, Kazimierz; Plebaniak, Robert; Banach, Artur
2009
Quasi-asymptotic contractions, set-valued dynamical systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces. (Quasi-asymptotic contractions, set-valued dynamic systems, uniqueness of endpoints and generalized pseudodistances in uniform spaces.) Zbl 1160.54011
Włodarczyk, Kazimierz; Plebaniak, Robert
2009
Endpoint theory for set-valued nonlinear asymptotic contractions with respect to generalized pseudodistances in uniform spaces. Zbl 1148.54021
Włodarczyk, Kazimierz; Plebaniak, Robert
2008
Generalized contractions of Meir-Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces. Zbl 1158.54005
Włodarczyk, Kazimierz; Plebaniak, Robert
2008
Existence and uniqueness of endpoints of closed set-valued asymptotic contractions in metric spaces. Zbl 1110.54025
Włodarczyk, K.; Klim, D.; Plebaniak, R.
2007
Endpoints of set-valued dynamical systems of asymptotic contractions of Meir-Keeler type and strict contractions in uniform spaces. Zbl 1124.54005
Włodarczyk, Kazimierz; Plebaniak, Robert; Obczyński, Cezary
2007
The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir-Keeler type in uniform spaces. Zbl 1202.54016
Włodarczyk, Kazimierz; Plebaniak, Robert; Obczyński, Cezary
2007
Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces. Zbl 1095.54019
Włodarczyk, K.; Obczyński, C.; Wardowski, D.
2006
Equilibria and fixed points of set-valued maps with nonconvex and noncompact domains and ranges. Zbl 1108.47047
Włodarczyk, K.; Klim, D.
2006
Fixed-point and coincidence theorems for set-valued maps with nonconvex or noncompact domains in topological vector spaces. Zbl 1020.47050
Włodarczyk, Kazimierz; Klim, Dorota
2003
Random iterations of holomorphic maps in complex Banach spaces. Zbl 0958.46026
Wlodarczyk, K.; Klim, D.; Gontarek, E.
2000
Random iterations of holomorphic contractions in locally convex spaces and of weaker contractions in uniform spaces. Zbl 0933.46040
Włodarczyk, Kazimierz; Gonicka, Joanna
1999
Angular derivatives of holomorphic maps in infinite dimensions. Zbl 0881.32004
Włodarczyk, Kazimierz; Szałowska, Alina
1996
Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains. Zbl 0802.46060
Włodarczyk, Kazimierz
1994
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of $$C^*$$-algebras. Zbl 0827.47030
Włodarczyk, Kazimierz
1994
The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces. Zbl 0817.46048
Włodarczyk, Kazimierz
1993
On the existence and uniqueness of fixed points for holomorphic maps in complex Banach spaces. Zbl 0744.47050
Włodarczyk, Kazimierz
1991
New extension of the Banach contraction principle to locally convex spaces and applications. Zbl 0654.47038
Włodarczyk, Kazimierz
1988
Approximative fixed points of compact holomorphic maps in complex Banach spaces. Zbl 0667.47033
Włodarczyk, Kazimierz
1988
Julia’s lemma and Wolff’s theorem for $$J^ *$$-algebras. Zbl 0621.46041
Włodarczyk, Kazimierz
1987
Studies of iterations of holomorphic maps in $$J^*$$-algebras and complex Hilbert spaces. Zbl 0595.47046
Włodarczyk, Kazimierz
1986
Pick-Julia theorems for holomorphic maps in $$J^ *$$-algebras and Hilbert spaces. Zbl 0612.46044
Włodarczyk, Kazimierz
1986
Iterations of holomorphic maps of infinite dimensional homogeneous domains. Zbl 0554.46019
Włodarczyk, Kazimierz
1985
On holomorphic maps in Banach spaces and $$J^*$$-algebras. Zbl 0595.46048
Włodarczyk, Kazimierz
1985
Some properties of analytic maps of operators in J*-algebras. Zbl 0521.46046
Wlodarczyk, Kazimierz
1983
all top 5


text:
510 views
Consider the following sequence of numbers:

$$92, 37, 52, 12, 11, 25$$

Use bubblesort to arrange the sequence in ascending order. Give the sequence at the end of each of the first five passes.
edited | 510 views
+2
$Remark:$
1. Bubble up the largest element to the end.
2. Array will be divided into two sorted and unsorted part.
3. If no swap happens in any of the pass, then terminate the procedure, and output all the elements.
4. Bubble sort is adaptive, stable and in-place algorithm.
+1

According to Cormen, moving smallest element to beginning

1st Pass:  11, 92, 37, 52, 12, 25

2nd Pass: 11, 12, 92, 37, 52, 25

3rd Pass: 11, 12, 25, 92, 37, 52

4th Pass: 11, 12, 25, 37, 92, 52

5th Pass: 11 12 25 37 52 92

$1$st Pass:  $37 \ 52 \ 12 \ 11 \ 25 \ 92$

$2$nd Pass: $37 \ 12 \ 11 \ 25 \ 52 \ 92$

$3$rd Pass: $12 \ 11 \ 25 \ 37 \ 52 \ 92$

$4$th Pass: $11 \ 12 \ 25 \ 37 \ 52 \ 92$

$5$th Pass: $11 \ 12 \ 25 \ 37 \ 52 \ 92$

Why 5 th pass ? In 4 th pass, the array is already sorted, but the algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted.

answered by Boss (19.9k points)
edited
0
Since 5 th pass is redundant, we can set a flag in such a way that we will come out of outer for loop after 4 passes ... in that cases only 4 passes ...
+2
How come? In 5th pass you will get to know there are no new swaps and hence the list must be sorted. If there would have been a 6th pass, it would be redundant.
+1 vote

1st Pass:  37 52 12 11 25 92

2nd Pass: 37 12 11 25 52 92

3rd Pass: 12 11 25 37 52 92

4th Pass: 11 12 25 37 52 92

5th Pass: 11 12 25 37 52 92

answered by Boss (11.7k points)

1
2


text:
# School of Mathematics

## Solutions to tutorial sheets

Solutions to tutorial sheets should appear here soon after the tutorial.

Links should open PDF format files.

Tutorial Sheet 1 [February 5]
Inverse and forward images. Example of an algebra.
Tutorial Sheet 2 [February 9]
Examples with the fact that $\mathscr L$ is a $\sigma$-algebra. Countable sets and the Cantor set included.
Basic examples of measurable functions. Compositions of continuos functions applied to measurable functions are measurable. Case of measurable functions defined on $[0,1]$/
Computing $\int_{\mathbb R} f \, d\mu$ via the Riemann integral (over finite closed intervals) and limits.


text:
Address 1635 Willow, Kingsland, TX 78639 (325) 388-3287 http://www.hitex.net

# gaussian error function integrals Valley Spring, Texas

For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). Both functions are overloaded to accept arguments of type float, double, and long double. The system returned: (22) Invalid argument The remote host or network may be down. When the error function is evaluated for arbitrary complex arguments z, the resulting complex error function is usually discussed in scaled form as the Faddeeva function: w ( z ) =

Please try the request again. M. and Watson, G.N. I did not know about the entropy-power inequality, so, thank you for adding that tool to my arsenal! –M.B.M.

p.297. Acton, F.S. MR0167642. Related functions The error function is essentially identical to the standard normal cumulative distribution function, denoted Φ, also named norm(x) by software languages, as they differ only by scaling and translation.

Perl: erf (for real arguments, using Cody's algorithm[20]) is implemented in the Perl module Math::SpecFun Python: Included since version 2.7 as math.erf() and math.erfc() for real arguments. Washington, DC: Hemisphere, pp.385-393, 1987. How to use the binomial theorem to calculate binomials with a negative exponent Can Communism become a stable economic strategy? Generalized error functions Graph of generalised error functions En(x): grey curve: E1(x) = (1−e−x)/ π {\displaystyle \scriptstyle {\sqrt {\pi }}} red curve: E2(x) = erf(x) green curve: E3(x) blue curve: E4(x)

Online Integral Calculator» Solve integrals with Wolfram|Alpha. Erf has the values (21) (22) It is an odd function (23) and satisfies (24) Erf may be expressed in terms of a confluent hypergeometric function of the first kind as The system returned: (22) Invalid argument The remote host or network may be down. The error function at +∞ is exactly 1 (see Gaussian integral).

Despite the name "imaginary error function", erfi  ( x ) {\displaystyle \operatorname  8 (x)} is real when x is real. The antiderivative of $e^{-t^2}$ is not $\frac{-1}{2t} e^{-t^2}$. –Rahul Sep 10 '11 at 5:41 3 @Angela, at the very least, it would be good of you to rewrite what you've Arfken, G. A complex generalization of is defined as (39) (40) Integral representations valid only in the upper half-plane are given by (41) (42) SEE ALSO: Dawson's Integral, Erfc, Erfi, Fresnel Integrals, Gaussian

Springer-Verlag. These generalised functions can equivalently be expressed for x>0 using the Gamma function and incomplete Gamma function: E n ( x ) = 1 π Γ ( n ) ( Γ IEEE Transactions on Wireless Communications, 4(2), 840–845, doi=10.1109/TWC.2003.814350. ^ Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". Does anyone know if this is solvable?

What is the first movie to show this hard work message at the very end? Despite the name "imaginary error function", erfi  ( x ) {\displaystyle \operatorname  8 (x)} is real when x is real. New York: Dover, pp.297-309, 1972. H.

Thank you all for your help with this! –M.B.M. When the error function is evaluated for arbitrary complex arguments z, the resulting complex error function is usually discussed in scaled form as the Faddeeva function: w ( z ) = Generalized error functions Graph of generalised error functions En(x): grey curve: E1(x) = (1−e−x)/ π {\displaystyle \scriptstyle {\sqrt {\pi }}} red curve: E2(x) = erf(x) green curve: E3(x) blue curve: E4(x) Math.

For complex, the Faddeeva package provides a C++ complex implementation. The defining integral cannot be evaluated in closed form in terms of elementary functions, but by expanding the integrand e−z2 into its Maclaurin series and integrating term by term, one obtains doi:10.1109/TCOMM.2011.072011.100049. ^ Numerical Recipes in Fortran 77: The Art of Scientific Computing (ISBN 0-521-43064-X), 1992, page 214, Cambridge University Press. ^ DlangScience/libcerf, A package for use with the D Programming language. Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments.

Generated Mon, 17 Oct 2016 03:52:32 GMT by s_wx1131 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ Connection Sep 12 '11 at 0:13 | show 1 more comment 2 Answers 2 active oldest votes up vote 10 down vote accepted $\operatorname{erf}(x)$ is an odd function, therefore, \begin{align} \int_{-\infty}^\infty(\operatorname{erf}(a+x)+\operatorname{erf}(a-x))\;\mathrm{d}x Mathematica: erf is implemented as Erf and Erfc in Mathematica for real and complex arguments, which are also available in Wolfram Alpha. Generated Mon, 17 Oct 2016 03:52:32 GMT by s_wx1131 (squid/3.5.20) J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans. The error function at +∞ is exactly 1 (see Gaussian integral). Princeton, NJ: Princeton University Press, p.105, 2003. ISBN0-486-61272-4. Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments. Level of Im(ƒ)=0 is shown with a thick green line. M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008). Supancic, "On Bürmann's Theorem and Its Application to Problems of Linear and Nonlinear Heat Transfer and Diffusion," The Mathematica Journal, 2014. Flow Chart with tikzpicture: particular tipes of arrows Appease Your Google Overlords: Draw the "G" Logo De kio “saluton” estas la rekta objekto? Another form of erfc  ( x ) {\displaystyle \operatorname  2 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc  ( x | x ≥ 0 Subtract 4a from (3) using (1) and (2) to get \int_{-\infty}^\infty\left(\operatorname{erf}(a+x)\operatorname{erf}(a-x)+1 \right)\;\mathrm{d}x =4a\operatorname{erf}(\sqrt{2}a)+\frac{2\sqrt{2}}{\sqrt{\pi}}\;e^{-2a^2}\tag{4}  My guess is you want either $(3)$ or $(4)$. Level of Im(ƒ)=0 is shown with a thick green line.

This directly results from the fact that the integrand e − t 2 {\displaystyle e^{-t^ − 2}} is an even function. All generalised error functions for n>0 look similar on the positive x side of the graph. After division by n!, all the En for odd n look similar (but not identical) to each other. D: A D package[16] exists providing efficient and accurate implementations of complex error functions, along with Dawson, Faddeeva, and Voigt functions.

Generated Mon, 17 Oct 2016 03:52:32 GMT by s_wx1131 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection ISBN978-1-4020-6948-2. ^ Winitzki, Sergei (6 February 2008). "A handy approximation for the error function and its inverse" (PDF). How to draw a path with coordinates defined by f(x) Can I release a pattern without releasing the whole held expression? J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN978-0521192255, MR2723248 External links MathWorld – Erf Authority control NDL: 00562553 Retrieved from

Schöpf and P. Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and R. (March 1, 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048,


text:
# [Tex/LaTex] Understanding xcolor color mixing model

color

I fail to understand the color mixing of xcolor.

I want to have a lighter and a darker version of a color defined as

\definecolor{BlueLUH}{cmyk}{1.0,0.7,0,0}

My approach of lighter and darker is this one

\colorlet{LightBlue}{BlueLUH!20!white}
\colorlet{DarkBlue}{BlueLUH!80!black!20}

which according to the docs is replaced internally to

\colorlet{LightBlue}{BlueLUH!20!white!white}
\colorlet{DarkBlue}{BlueLUH!80!black!20!white}

Now I wonder what is actually calulated, bcause I get the same for Light and Dark, as can be seen in the following screenshot:

That are different colors, but cannot be seen! 20% of black is less than light gray! Compare it with a 40% of black! The values for the cmyk color can easily be seen in the pdf output when using \pdfcompresslevel=0.

The colors are calculated as:

\pdfcompresslevel=0
\documentclass{article}
\usepackage[cmyk]{xcolor}

\definecolor{BlueLUH}{cmyk}{1.0,0.7,0,0}
\colorlet{LightBlue}{BlueLUH!20!white}
\colorlet{DarkBlue}{BlueLUH!80!black!20}
%\colorlet{LightBlue}{BlueLUH!20!white!white}
%\colorlet{DarkBlue}{BlueLUH!80!black!20!white}

\begin{document}

\color{BlueLUH}\rule{1cm}{1cm}
\color{LightBlue}\rule{1cm}{1cm}
\color{DarkBlue}\rule{1cm}{1cm}

\color[cmyk]{1, 0.7, 0, 0}\rule{1cm}{1cm}
\color[cmyk]{0.2, 0.14, 0, 0}\rule{1cm}{1cm}
\color[cmyk]{0.16, 0.112, 0, 0.04}\rule{1cm}{1cm}

\colorlet{DarkBlue}{BlueLUH!80!black!40}
\color{BlueLUH}\rule{1cm}{1cm}
\color{LightBlue}\rule{1cm}{1cm}
\color{DarkBlue}\rule{1cm}{1cm}

\end{document}


text:
# Circular motion of a train

by tyro008
Tags: circular, motion, train
 P: 20 1. The problem statement, all variables and given/known data A train is rounding a circular curve whose radius is 2.00 X 10$$_{}2$$ m. At one instant, the train has an angular acceleration of 1.50 X 10^-3 rad/s$$_{}2$$ and an angular speed of 0.0400 rad/s. (a) Find the magnitude of the total acceleration (centripetal plus tangential) of the train. (b) Determine the angle of the total acceleration relative to the radial direction. 2. Relevant equations a$$_{}NET$$ = $$\sqrt{}ac2^{}_{} + at2^{}$$ and Ac is the centripetal acceleration, At is the tangential acceleration 3. The attempt at a solution i tried using this equation, but i couldn't find At. to find this, you need delta velocity divided by delta time, but there is no time and i don't know if angular speed is the same thing as regular velocity