text:
# Definition:Infimum

## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

Infimum may refer to:

## Also known as

Particularly in the field of analysis, the infimum of a set $T$ is often referred to as the greatest lower bound of $T$ and denoted $\map {\mathrm {glb} } T$ or $\map {\mathrm {g.l.b.} } T$.

Some sources refer to the infimum of a set as the infimum on a set.

Some sources introduce the notation $\displaystyle \inf_{y \mathop \in S} y$, which may improve clarity in some circumstances.

Some older sources, applying the concept to a (strictly) decreasing real sequence, refer to a infimum as a lower limit.

## Also defined as

Some sources refer to the infimum as being the lower bound.

Using this convention, any element less than this is not considered to be a lower bound.

## Linguistic Note

The plural of infimum is infima, although the (incorrect) form infimums can occasionally be found if you look hard enough.


text:
# Tag Info

11

Subsequential edits within five minutes of the initial edit are combined into that edit. So if you post a question or answer, and then read it after posting (which for some reason may involve a different state of mind than while editing) and find a mistake, then go ahead and fix it within these five minutes. Of course, the question will get bumped to the ...

10

The user made an edit, then before five minutes (the "grace period") passed reverted it (but not via the "rollback" feature). In general if you do multiple edits within the five minutes window they only count as one. If the net result is that nothing changed, there's no difference to show in the revisions window, but the system still records the fact that ...

8

This is kinda intentional; if you don't change anything, it feels odd to record a change record. Indeed: you can't edit the revision history, but in the general case, that is probably a good thing anyway. I'm not sure this is going to cause a real problem very often - or at least, it seems more likely to be misused by changing revision reasons. As a rule of ...

7

Links to the review-summaries of the edits a user suggested are recorded on the user's page; these include a record of the proposed edit. The list of suggested edits is the "suggestion" tab on the "all actions" tab.

6

Does not seem like a bug. Edits done withing five minutes by the same user after posting or an initial edit are put together in one revision to avoid cluttering the revision history. (Except if somebody comments on a post in the interim. Then a new revision is created to avoid confusion over comments that refer to a part of the post that then gets changed.)...

6

When a question gets reopened it is pushed to the top of the "active" list. This modification, the reopening, is assigned to the last (I think, or at least some) user that voted to reopen. See the question's revision history to see the reopening involving Bill Dubuque just at that time.

5

From what I have learned today editing of an answer is to be used with discretion, and is not meant to be used as a sandbox in which to develop your (half) answer over a few hours (days (weeks (months(...)))) or so. (This also applies to editing questions, but my post was essentially about editing answers.) I have been looking at some of my past posts and ...

4

If you don't mind installing a userscript in your browser, you can use one of the existing userscripts. SE Modifications — Username autocomplete in comments, inline revision source, and utility links adds a history link below every post if there isn't one already (as well as other features). Add Hidden Links is more specialized. Add Δimeline and ℜevisions ...

3

If the question was edited, there's a link to the revision history, just like there will be with undeleted answers. In this case, https://math.stackexchange.com/posts/1680571/revisions And if it wasn't edited, then using https://math.stackexchange.com/posts/<answer number here>/revisions will work just fine. You can also access the timeline by ...

3

In the url, there is always the post number (this is post 6196). You can go to ...stackexchange.com/posts/(post number)/revisions where I put "posts" in italics to indicate that it changes too. For example, this post has never been edited, but you can go to https://math.meta.stackexchange.com/posts/6196/revisions for this question.

3

For the specific case: seconding John Ma, the last edit (by Will R.) actually clarifies the situation. The earlier addition(s) of "positive" however was besides the point. For the general question: there is no point in engaging in back-and-forth editing. It's just noise. Stop editing around (everybody). In case there is a conflict, make your case in a ...

1

The problem is caused by the green and red highlighting, if you look closely, you can see $'s in them. These$ aren't counted properly as MathJax, and therefor, the whole rendering breaks down. Fixing this would probably require a change in core Stack Exchange code, we could consider asking on Meta Stack Exchange as a feature request? I'm not positive on ...

Only top voted, non community-wiki answers of a minimum length are eligible

format: plain


text:
• Create Account

### #Actualtanzanite7

Posted 15 January 2013 - 04:45 PM

"foo(7*6)" with reference to non-const "foo" function gives in VC: "initial value of reference to non-const must be an lvalue" - perfectly reasonable. Did not realize compiler is willing to create a new temporary constant object in this case - thanks, me likes.

However. My actual Emit::get() code is like:
Wrap<T> get() {
Wrap<T> result;
... more stuff
return result;
}

The internal copy of "result" may not be destroyed before it is returned - i fail to see the relevance of the given example (call me dense). I do not see any reason why the compiler would care what happens with "result" before it is destroyed - Wrap<T> destructor tells all it needs to know. Ie. it is not a compiler temporary created for referencing purposes - it is local variable which also happens to be returned and hopefully short-circuited by return value optimization.

Also, using "explicit" and forcing it to use the correct copy constructor does get around that problem (plugged into my actual code and it passed all my test cases - as far as i can see it does exactly what i expect it to do). Acceptable workaround (would prefer the constructor not being "explicit" tho).

Assignment, however is much more problematic (no "explicit" keyword to hide the "wrong" one) - if i comment the other one out, and hence force it to use the right one, then it works. Cannot make the type conversion explicit either (that would fix all the problem without needing any workarounds, unfortunately - not an acceptable loss).

Irritating. Prefers a function it can only use through implicit type conversion to the function that matches from start :/.

3) Unusual, perhaps, but perfectly reasonable. It is not copy-assignment nor move-assignment (it only looks like move assignment because it is a minimized example-case) - it is just an assignment that does stuff that is expected to happen when one uses assignment with the relevant object types.

1) If you try to force the language to do the unexpected, like having something that looks like like it might be an assignment operator not have the signature of an assignment operator and not work like an assignment operator, you should really expect your program to do the unexpected.

2) Also, there is a significant difference between a const reference and a reference to a const. One is "int const&" the other is "int& const"... can you guess which is which, and which one "const int&" is?

1) Unexpected != unusual. One would fully expect that particular class to behave exactly the way it does. What the hell are you blabbering about?
2) You did not pay any attention to what i have said, right? I know perfectly well what is what - i had problems digesting a response where parts of it made no sense.

why do you refer to "reference to non-const" as "non-const reference"?

Because that's how the rest of the world typically does it (at least in English). I guess you could technically call it a misnomer, maybe, but references themselves are always const (so it makes no sense to have a truly "non-const reference" (that is, a reference that can be changed to refer to another object; it's impossible in C++)), so when people talk about (non) const references, the (non) const always refers to the object that the reference refers to, not to the reference itself (since the reference itself is always const).

Thanks for the explanation. Is it something that is accepted in English CS classes? Correct terminology was quite important for us - unfortunately, none of it was in English, so i tend to be cautiously confused when i encounter something in English that does not seem to make any sense.

I recommend you and everyone else drop the incorrect usage - impossibility of "non-const reference" is an unacceptable reason to refrain using the perfectly valid "reference to const". VC agrees with me and also uses "reference to const" ;).

Sorry if i am too picky here.

edit: un-fuckup the forum formatting.

### #1tanzanite7

Posted 15 January 2013 - 04:45 PM

"foo(7*6)" with reference to non-const "foo" function gives in VC: "initial value of reference to non-const must be an lvalue" - perfectly reasonable. Did not realize compiler is willing to create a new temporary constant object in this case - thanks, me likes.

However. My actual Emit::get() code is like:

Wrap<T> get() {
Wrap<T> result;
... more stuff
return result;
}

The internal copy of "result" may not be destroyed before it is returned - i fail to see the relevance of the given example (call me dense). I do not see any reason why the compiler would care what happens with "result" before it is destroyed - Wrap<T> destructor tells all it needs to know. Ie. it is not a compiler temporary created for referencing purposes - it is local variable which also happens to be returned and hopefully short-circuited by return value optimization.

Also, using "explicit" and forcing it to use the correct copy constructor does get around that problem (plugged into my actual code and it passed all my test cases - as far as i can see it does exactly what i expect it to do). Acceptable workaround (would prefer the constructor not being "explicit" tho).

Assignment, however is much more problematic (no "explicit" keyword to hide the "wrong" one) - if i comment the other one out, and hence force it to use the right one, then it works. Cannot make the type conversion explicit either  (that would fix all the problem without needing any workarounds, unfortunately - not an acceptable loss).

Irritating. Prefers a function it can only use through implicit type conversion to the function that matches from start :/.

3) Unusual, perhaps, but perfectly reasonable. It is not copy-assignment nor move-assignment (it only looks like move assignment because it is a minimized example-case) - it is just an assignment that does stuff that is expected to happen when one uses assignment with the relevant object types.

1) If you try to force the language to do the unexpected, like having something that looks like like it might be an assignment operator not have the signature of an assignment operator and not work like an assignment operator, you should really expect your program to do the unexpected.

2) Also, there is a significant difference between a const reference and a reference to a const. One is "int const&" the other is "int& const"... can you guess which is which, and which one "const int&" is?

1) Unexpected != unusual. One would fully expect that particular class to behave exactly the way it does. What the hell are you blabbering about?
2) You did not pay any attention to what i have said, right? I know perfectly well what is what - i had problems digesting a response where parts of it made no sense.

why do you refer to "reference to non-const" as "non-const reference"?

Because that's how the rest of the world typically does it (at least in English). I guess you could technically call it a misnomer, maybe, but references themselves are always const (so it makes no sense to have a truly "non-const reference" (that is, a reference that can be changed to refer to another object; it's impossible in C++)), so when people talk about (non) const references, the (non) const always refers to the object that the reference refers to, not to the reference itself (since the reference itself is always const).

Thanks for the explanation. Is it something that is accepted in English CS classes? Correct terminology was quite important for us - unfortunately, none of it was in English, so i tend to be cautiously confused when i encounter something in English that does not seem to make any sense.

I recommend you and everyone else drop the incorrect usage - impossibility of "non-const reference" is an unacceptable reason to refrain using the perfectly valid "reference to const". VC agrees with me and also uses "reference to const" ;).

Sorry if i am too picky here.

PARTNERS


text:
# Lagrangian is a function of

1. Apr 14, 2014

### astro2cosmos

Lagrangian is a function of ......

Since Lagrangian is a function of q, q dot & time, then why in describing the Hamiltonian (H), L does not involve time explicitly????
as H = (p*q dot) - L (q, q dot).

2. Apr 14, 2014

### Einj

It should. The crucial point is that, if the Lagrangian doesn't depend explicitly on time then the Hamiltonian coincides with the energy of the system. However, H is defined also when L explicitly depends on t.

3. Apr 14, 2014

### fisicist

astro2cosmos, where did you get that equation from? Formally, the Hamiltonian is generated from the Lagrangian by doing a Legendre transform (If you replacy only some of the generalized coordinates by their conjugate momentums, you get a Routh's function, by the way), see Arnol'd or, for a simpler treatment, Landau/Lifshitz; So what should prevent you from treating additional variables? What is true anyway, is

$\frac{\partial \mathcal H}{\partial t} = \frac{\mathrm d \mathcal H}{\mathrm d t}$.

Besides that, in a closed inertial system, time is homogenous.

4. Apr 14, 2014

### fisicist

Forgotten: For any parameter, including time, the following relation is true:

$\left( \frac{\partial \mathcal H}{\partial \lambda} \right)_{p, q} = - \left( \frac{\partial \mathcal L}{\partial \lambda} \right)_{p, q}$

5. Apr 14, 2014

### vanhees71

The Lagrangian and the Hamiltonian both can also be explicitly time dependent. The Lagrangian is a function of $q$, $\dot{q}$, and (sometimes) of time. The Hamiltonian is the Legendre transformation of the Lagrangian wrt. $\dot{q}$ vs. the canonical momentum
$$p=\frac{\partial L}{\partial \dot{q}},$$
i.e.,
$$H=p \cdot \dot{q}-L.$$
The total differential is
$$\mathrm{d} H=\mathrm{d}p \cdot \dot{q} + p \cdot \mathrm{d} \dot{q}-\mathrm{d} q \cdot \frac{\partial L}{\partial q}-\mathrm{d} \dot{q} \cdot \frac{\partial L}{\partial \dot{q}}-\mathrm{d} t \frac{\partial L}{\partial t}=p \cdot \mathrm{d} \dot{q}-\mathrm{d} q \cdot \frac{\partial L}{\partial q}-\mathrm{d} t \frac{\partial L}{\partial t}.$$
From this you read off that the "natural variables" for $H$ are indeed $q$, $p$, and $t$, and that the following relations hold
$$\left (\frac{\partial H}{\partial p} \right)_{q,t}=\dot{q}, \quad \left (\frac{\partial H}{\partial q} \right)_{p,t}=-\left (\frac{\partial L}{\partial q} \right )_{\dot{q},t}, \quad \left (\frac{\partial H}{\partial t} \right )_{q,p}=-\left (\frac{\partial L}{\partial t} \right)_{q,\dot{q}}.$$
It is important to keep in mind that in the latter relations different variables are kept fixed when the partial derivative wrt. to the pertinent variable is taken on both sides of this equation! That's why I put the variables to be hold fixed in the different cases as subscipts of the parantheses around the partial derivative explicitly!

6. Apr 16, 2014

### astro2cosmos

for what condition L is independent of time?????

7. Apr 16, 2014

### UltrafastPED

8. Apr 18, 2014


text:
## Algebra 1: Common Core (15th Edition)

$c=1/5$
We first add 4c to both sides to get that $4+10c=6$. We then subtract 4 on both sides to get that $10c=2$. We finally divide by 10 to get that $c=2/10$, which equals 1/5.


text:
Moore–Penrose inverse for constrained least squares

I would like to use the generalized Moore–Penrose inverse for solving a constrained least squares problem. More explicitly, I need to find the matrix A minimizing ||AX-B||, where matrices X and B are given. The problem is that components of matrices X and B are in [0,1] while components of A must be in [-1,1]. Any idea how to deal with this problem?

• I realize the pseudoinverse solves least squares problems, but what makes you think it can be used to solve constrained least squares problems? I haven't seen that before, although it would be interesting if it turns out to be true. – littleO Oct 11 '17 at 20:11
• Do you mean that the components of $X$ (rather than $A$) are constrained to belong to $[-1,1]$? – littleO Oct 11 '17 at 20:12
• I have no reason to think that it can be possible and perhaps I am forcing the use of the pseudo-inverse to solve that problem. – Gonzalo Nápoles Oct 11 '17 at 20:16
• X and B are always in [0,1] and they are my inputs, so I must be able to find a matrix A in [-1,1] minimizing the expression above. – Gonzalo Nápoles Oct 11 '17 at 20:18
• Oh, I see. It's unusual notation to have $X$ be given and have $A$ be the unknown. Most people would expect the opposite. – littleO Oct 11 '17 at 20:19


text:
# Math Help - Vector

1. Originally Posted by Gamma
Are you talking about the other question on the other Thread? I am really confused as to what you are talking about? Again I cannot stress enough, there is no "THE basis" there is no preferred basis, it is just a basis.

If you need to find a basis for $\mathbb{R}^n$,just pick the standard basis for $\mathbb{R}^n$.
{(1,0,...,0), (0,1,0,...,0),... (0,0,...,1)}
I was talking about this post. What i wanted to understand is how can i derive a standard basis for this, how can i find the rank of every row how can i know which rows have pivot?
Thanks
KC

2. ## Definition

Man, I am really lost with what you are asking now. I think you need to review some of your definitions, it is getting to the point that these posts are becoming incoherent to me.

You do not find a basis for a matrix.

A matrix represents a linear transformation, a basis is for a vector space, not a function. Matrices have ranks, it does not make sense to talk about the rank of a row.

The dual space to $\mathbb{R}^n$ does not have a "standard" basis. It is not canonically isomorphic to $\mathbb{R}^n$. It is isomorphic, but only in terms of a basis. If you give me a basis for $\mathbb{R}^n$, I will give you a basis for $(\mathbb{R}^n)^*$.

I already wrote out the basis for the dual space in a previous post on here titled "bassis(I can't type apparently) for the Dual Space".

Look at that. If you want the basis for the dual space for $\mathbb{R}^n$ subordinant to the standard basis, then $e_1=(1,0,0,...,0)$
$e_2=(0,1,0,...,0)$
.
.
.
$e_n=(0,0,0,...,1)$

and this yields the basis for $(\mathbb{R}^n)^*$
$\epsilon_1(a_1e_1+a_2e_2+...+a_ne_n)=a_1$
$\epsilon_2(a_1e_1+a_2e_2+...+a_ne_n)=a_2$
.
.
.
$\epsilon_n(a_1e_1+a_2e_2+...+a_ne_n)=a_n$

3. Originally Posted by Gamma
This is the point, it depends on the basis, there are an infinite number of possible choices for basis of $\mathbb{R}^n$ each of these yields a different basis for $(\mathbb{R}^n)^*$.

To give you the idea though for any given basis for $\mathbb{R}^n$ call it $\{e_1,e_2,...,e_n\}$, you get n linear functionals in $(\mathbb{R}^n)^*$ that will form the basis, say they are $\{\epsilon^1,\epsilon^2,...,\epsilon^n \}.$

Let the n functionals be defined as follows.

$\epsilon^i(a_1e_1 +a_2e_2 + ... + a_ie_i + ... +a_ne_n)=a_i$

Yeah, there is your basis. If you took the standard basis for $\mathbb{R}^n$ the ith coordinate function would simply pick out the ith coefficient.

could you please explain to me in a little more detail on how i can find the basis for this.
thanks

Page 2 of 2 First 12


text:
# Centering Figure without re-scale [duplicate]

I would like to center a figure made on Tikz. This figure has a specific size which is wider than \textwidth, and it needs to be centered. All options I see use \resibox or \makebox to center the figures. But I don't want to change the figure size. Are there any option or command to allow this?

Thanks very much in advance. Kind regards,

German

=== SOLUTION == As Mr @David Carlisle commented below, the solution is uncomment the \makebox and set the scaling to 0pt as follow:

\begin{figure}[h!]
\centering
\newlength\figureheight
\newlength\figurewidth
\setlength\figureheight{6cm}
\setlength\figurewidth{1.2\linewidth}
\begingroup
\fontsize{8}{\baselinestretch}\selectfont
\makebox[0pt][c]{
\input{VoltFRFFreq.tikz}
%}
\endgroup
\caption{A plot of a sphere}
\label{fig.freq}
\end{figure}

Thanks again to all people!!

-- EDIT's --- P.D.-I forgot to mention I use XeLaTeX, I hope it helps. Kind regards, P.D.D- The code is

\begin{figure}[h!]
\centering
\newlength\figureheight
\newlength\figurewidth
\setlength\figureheight{6cm}
\setlength\figurewidth{1.2\linewidth}
\begingroup
\fontsize{8}{\baselinestretch}\selectfont
%\makebox[\figurewidth][c]{
\input{VoltFRFFreq.tikz}
%}
\endgroup
\caption{A plot of a sphere}
\label{fig.freq}
\end{figure}

## marked as duplicate by David Carlisle floats StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 24 '16 at 19:19

uncomment your \makebox

  %\makebox[\figurewidth][c]{

but change the specified width to 0pt instead of \figurewidth

since your figure is wider than the text width, you want to make it look to latex like it is narrower. here's one possibility (just the group with the figure):

\noindent\hss
\begingroup
\fontsize{8}{\baselinestretch}\selectfont
\input{VoltFRFFreq.tikz}
\endgroup
\hss\par

• Hi Barbara The code you propose gives me an error: ! Infinite glue shrinkage found in a paragraph. I forgot to mention I use XeLaTeX, I hope it helps. Kind regards, – Germán Martínez Jun 24 '16 at 18:19
• david's answer is more "real latex". so go with that. this one could be salvaged by changing the \hss to something like \hskip -.15\linewidth (or, better, \hspace{-.15\linewidth}) but the latex \makebox with 0 width does the "right thing". xelatex doesn't matter in this situation. – barbara beeton Jun 24 '16 at 19:03


text:
Cost of the NAPLEX

Approximately, the cost of taking the NAPLEX is $575 and the fee for the MPJE is$200. This fee increases, approximately every 5 years.


text:
UK Secondary (7-11)
Surface area of cylinder I
Lesson

Like finding the surface area of a prism the surface area of a cylinder uses a similar process.

Let's see how it would look if we open up a cylinder to view its net.

Notice that when the curved surface is unfolded, it becomes a rectangle. By rotating the circle on top of the rectangle, can you see how the circumference of the circle is equal to the length of the rectangular piece?

This means that we can break down the total surface area of a cylinder in the following way:

Surface Area of a Cylinder = Area of 2 circular ends  + Area of 1 rectangular piece

= $\left(2\times\pi r^2\right)+\left(L\times W\right)$(2×πr2)+(L×W)

Area of each circle: the radius of each circle is the same as the radius of the cylinder

Area of the rectangle: the width of the rectangle corresponds to the height of the prism, while the length of the rectangle is the circumference of the circle ( $2\pi r$2πr )

Surface Area of a Cylinder

$\text{Surface Area of a Cylinder }=2\pi r^2+2\pi rh$Surface Area of a Cylinder =2πr2+2πrh

#### Worked Examples

##### QUESTION 1

Consider the following cylinder with a height of $35$35 cm and base radius of $10$10 cm. Find the surface area of the cylinder.

A cylindrical can of radius $7$7 cm and height $10$10 cm is open at one end. What is the external surface area of the can correct to two decimal places?


text:
# Seed to flower/mushroom

I've already done quite a bit of cleaning up. For example, the strings dryCheck and blueCheck no longer exist, instead they're replaced with "else". But I think this could be done 10x better, so if you know how (no advanced C++ lingo etc), that would be great!

A red seed will grow into a flower when planted in soil temperatures above 75 degrees, otherwise it will grow into a mushroom. Assuming the temperature meets the conditions for growing a flower, planting a red seed in wet soil will produce a sunflower and planting a red seed in dry soil will produce dandelion. A blue seed will grow into a flower when planted in soil temperatures ranging from 60 to 70 degrees, otherwise it will grow into a mushroom. Assuming the temperature meets the conditions for growing a flower, planting a blue seed in wet soil will produce a dandelion and planting the blue seed in dry soil will produce a sunflower. Write a program that will ask the user to input the seed color, the soil temperature and whether the soil is wet or dry and then output the plant that will grow.

#include <iostream>
#include <string>
using namespace std;

int main()
{
string seedColor, soilMoist, redCheck, wetCheck;
int soilTemp;

redCheck = "Red";
wetCheck = "Wet";
cout << "Enter the seed type (Blue/Red): ";
getline(cin, seedColor);

cout << "Enter the soil temperature: ";
cin >> soilTemp;

cout << "Is the soil dry or wet? ";
cin >> soilMoist; // I tried another "getline(cin, soilMoist), but that conflicts with the cin >> soilTemp; (line 30)

if (seedColor == redCheck)
{
if (soilTemp > 75)
{
if (soilMoist == wetCheck)
cout << "It's a sunflower!";
else
cout << "It's a dandelion!";
}
else
cout << "It's a mushroom!";
}

else
{
if (60 < soilTemp && soilTemp < 70)
{
if (soilMoist == wetCheck)
cout << "It's a dandelion!";
else
cout << "It's a sunflower!";
}
else cout << "It's a mushroom!";
}
}

• Welcome to Code Review! We're glad you found our site. It's best to write a title that will say something about what your code does, as you can see we have made a few edits. I hope you get some great reviews! – Phrancis Jan 30 '15 at 23:00
• @Phrancis Alright, thanks! The title makes more sense now, yes xD – Jack Jan 31 '15 at 8:39

Just some quick pointers here to get the more obvious details out of the way. First, you should not use using namespace std;, but rather explicitly state which namespace you are using like this std::cout. This prevents namespace clashes, and is discussed in great detail here.

Second, you should use braces around your if/else statements and loops even when there is only one statement after it:

if (soilMoist == wetCheck)
cout << "It's a sunflower!";
else
cout << "It's a dandelion!";

Should be:

if (soilMoist == wetCheck)
{
std::cout << "It's a sunflower!";
}
else
{
std::cout << "It's a dandelion!";
}

Right here, you should not indent your braces:

if (soilTemp > 75)
{
if (soilMoist == wetCheck)
cout << "It's a sunflower!";
else
cout << "It's a dandelion!";
}

You do not do this in other areas, so I don't know why you did it here.

You should also not indent your cins:

cout << "Enter the soil temperature: ";
cin >> soilTemp;

You should have your prompts always specify exactly what the input should be. Here, it looks as if you expect lowercase input: "Is the soil dry or wet? " However, the program checks for uppercase input. The best way to fix this would be to allow both "wet" or "Wet".

Otherwise, this looks pretty good. However, one way you may want to consider expanding your program in is ensuring the user put in the right values instead of merely assuming the right values will be input. You could do this with a do-while loop, among other ways.

This code is an example of what I mean:

string input = "";

do {
if (input == "")
{
std::cout << "Is the soil dry or wet? ";
}
else
{
std::cout << "Invalid response.\nIs the soil dry or wet? ";
}

std::cin >> input;

} while (input != "Wet" && input != "wet");

• Most of these are stylistic preferences and neither right nor wrong. I would elaborate on your point about verifying input. Specifically that he is prompting for wet (lowercase w) but expecting Wet(uppercase W). – Kevin Jan 31 '15 at 2:58
• @Hosch250 I heard that I used braces in a weird way. I thought the indents didn't matter at all, they just help me keeping track of what output belongs to what if or else, like I said, only my 3rd week so I lose track of stuff easily. I know I should've used braces around if and else, but it just didn't seem neccesary right now (bad coding, I know). And finally the using namespace std; was just recommended everywhere on tutorials and stuff, so I didn't really think it would be bad, but I'll make sure to change it. Thanks! – Jack Jan 31 '15 at 8:07
• @Kevin How would I verify the input? Because indeed, when I input "wet" (lowercase) it will see it as false and go to else (dry). – Jack Jan 31 '15 at 8:08
• @Hosch250 Ah I see know what you mean with indenting the braces, it looks a lot better when they're back one tab! :D – Jack Jan 31 '15 at 8:25
• @jack there's a couple of things you could do. One way would be to compare the input to your two expected inputs and then re-prompt in a while loop until it matches one of the two. You could also be more forgiving and compare the input to Wet or wet. Also, as for the brackets and indenting, the important thing is to be clean and consistent so it is easy to read. Also, if you are working with existing code, go with the style that is already there, don't mix in a different style. – Kevin Jan 31 '15 at 14:33


text:
My Math Forum LP with Big-M Method
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 May 23rd, 2012, 01:28 AM #1 Member   Joined: Jan 2010 Posts: 44 Thanks: 0 LP with Big-M Method Hello! Have some difficulties to obtain some properties of optimal solution for one LP with respect to the other. So - I have a LP: min$cx$ s.t. $Ax=b$, $x\geq 0$ I apply the Big M method to get initial basic feasible solution, so I get a LP': min$cx+M\sum_{i=1}^m{y_i}$, where M is large number s.t. $Ax+y=b$, $x,y\geq 0$ Simplex algorithm is applied. 1)In all text-books it is said, that one can easily see, that if LP' has an optimal solution with y\neq 0, then LP is unfeasible. Why is that? 2)If it is known that LP' is not bounded, then it follows LP is unbounded or unfeasible. What is justification for that? Maybe someone can explain or give a hint?

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text:
Wanna get boxed?

Algebra Level 2

If $a^{2} + ab + b^{2} = 19$ $a^{4}+a^{2}b^{2}+b^{4} = 133$

then what is the value of $$\boxed{ab}$$ $$?$$

×

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# How do you use the laws of exponents to simplify the expression 4^40/4^20?

##### 1 Answer
Apr 30, 2015

In this way:

${4}^{40} / {4}^{20} = {4}^{40 - 20} = {4}^{20}$.


text:
## Wikipedia - Mobilità elettrica (it) electric mobility, $$u$$, $$\mu$$

https://doi.org/10.1351/goldbook.E01932
Speed of ions divided by the electric field strength in the phase concerned.


text:
# Quark Matter 2014 - XXIV International Conference on Ultrarelativistic Nucleus-Nucleus Collisions

19-24 May 2014
Europe/Zurich timezone

## Centrality dependence of the J/$\psi$ production in p-Pb collisions with ALICE at the LHC

20 May 2014, 16:30
2h

### spectrum

Board: F-26
Poster Open Heavy Flavour and Quarkonia

### Speaker

Igor Lakomov (Universite de Paris-Sud 11 (FR))

### Description

The study of proton-nucleus collision at LHC energies represents an important step in Quark-Gluon Plasma related studies, allowing a quantitative evaluation of cold nuclear matter effects on various observables. The ALICE Collaboration is carrying out a comprehensive study on charmonium production in p-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV in the dimuon decay channel. The analysis of the centrality dependence of the J/$\psi$ production is now in progress. Various centrality-related observables are being investigated, and their use in the charmonium analysis is being evaluated. In this poster, we will discuss the present status of the study of the centrality dependence of the J/$\psi$ production in p-Pb collisions, including an estimate of the $\langle p_{\rm} \rangle$ evolution with centrality.
On behalf of collaboration: ALICE

### Primary author

Igor Lakomov (Universite de Paris-Sud 11 (FR))

 Poster


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## Resources for 3D Printing with the MP Select Mini

Posted on March 23, 2017   ·   0 min read   ·   #3d printing

What’s better than an inexpensive 3D printer? Free sources of information! The items below are a resource list for 3D printing with the Monoprice Select Mini, all thanks to a lively community of users around the interwebz.

# General Info

• Product Page:
• Official User Manual:
• Reddit:
• Unofficial Wiki:
• Community Knowledge Base:

# Materials and Accessories

• Tested PLA Brands:
• Alternative Bed Surface:

# Initial Set Up

• CAD Modeling Software (free for hobbyists and enthusiasts):
• Slicing Software:
• Onboard WiFi for wireless printing:
• Using Raspberry Pi and Octoprint for wireless printing:

# Machine Settings

## General

The machine settings below are based off the ones in the official user manual. However, the start and end gcode was taken from the community-driven Google Doc (see above) and slightly modified to include an initial nozzle wipe/primer and to remove the delay in turning the fans off.

Machine settings for MP Select Mini.

For the lazy, you can simply copy and paste the code boxes below (ignore the End Gcode in the image above).

;; Start Gcode
G28 ;Home
G1 Z0.2 F1200 ; raise nozzle
G92 E0 ; reset extrusion distance
G1 X10
G1 Y100 E12 F600 ; purge nozzle & wipe
G92 E0 ; reset extrusion distance

;; End Gcode
M104 S0 ; turn off hotend heater
M140 S0 ; turn off bed heater
G91 ; Switch to use Relative Coordinates
G1 E-2 F300 ; retract the filament a bit before lifting the nozzle to release some of the pressure
G1 Z1 ; raise Z 1mm from current position
G1 E-2 F300 ; retract filament even more
G90 ; Switch back to using Absolute Coordinates
G1 X20 ; move X axis close to tower but hopefully far enough to keep the fan from rattling
G1 Y115 ; move bed forward for easier part removal
M84 ; disable motors
G4 S600 ; keep fan running for 600 seconds to cool hotend and allow the fan to be turned off
M107 ; turn off fan

## OctoPrint

To connect OctoPrint through Cura, go to “Settings > Printer > Manage Printers”, select your printer from the list, then click the “Connect OctoPrint” button on the right side of the menu.

Setting up OctoPrint through Cura.

This way, you can send gcode files directly from Cura to Octoprint with a click of a button!

# Print Settings

When fiddling with layer heights, it’s recommended to use the optimal values below:

• 0.04375 (results may vary)*
• 0.0875
• 0.13125
• 0.175
• 0.21875
• 0.2625
• 0.30625

Numbers courtesy of Michael O’Brien on Hackaday. Explanation:

So that motor [Z-Axis] is a 7.5°, 48 step motor as I just listed. Since the motor is attached to a M4 rod, which has a 0.7 mm thread pitch, then in one revolution makes the Z-Axis travel up or down 0.7 mm. Since it took 48 steps to turn that rev, each step is 0.0014583… mm. To avoid rounding errors, you can use multiple of 3 of this number, which is a nice and pretty 0.04375 mm. That is a nice and handy number that effectively represents the layer heights that mathematically work the best for layer heights for this printer.

The settings below should serve as a decent starting point in dialing in your own print settings for PLA.

PLA material settings.

# Design Guidelines

Want parts to fit together? 0.25mm is usually works well.

For mating parts, a general guideline of 0.25mm is sufficient.

# Troubleshooting

## Hole Features on First Layer Not Adhering

Make the following setting modifications, in descending order of preference (I try to avoid using rafts to reduce print time and material waste).

• Slow down print speed to ~10mm/s
• Increase build plate temperature and/or use external adhesion methods (ie. glue/hairspray)
• Increase initial layer height such that more material sticks to the bed
• Disable fans for initial layer
• Use raft

## Stringy Parts

• Fiddle with retraction distance and speed (start with 4.5mm and 40mm/s)

Last edited: February 10, 2018


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# Fermat Prime?

Find all triples $$(p,n,k)$$ of positive integers, where $$p$$ is a Fermat's Prime, satisfying

$\large{p^n + n = (n+1)^k}$

Observation: a Fermat's Prime is a prime number of the form $$2^{\alpha} + 1$$, for $$\alpha$$ positive integer.

×


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## Sunday, February 14, 2016

### Port Forwarding in Mythbuntu

My MythTV setup recently broke in an "interesting" way, and the fix I came up with is a bit involved ... so be warned, what follows is a major kludge.

### Setup

Before explaining the pathology (and fix), I need to describe the setup. I have Mythbuntu installed on a PC whose only function is to serve as a digital video recorder (DVR). The PC connects to my home WiFi LAN, but the connection is occasionally unstable. I'm not sure if the problem lies with the USB WiFi modem, a driver, or some obscure setting.

Both the lone MythTV back end and the lone MythTV front end run on the PC, with the back end configured to use a static IP address. When watching recordings, I use MythMote on my (Android) phone as a remote control. MythMote connects to the back end via WiFi. Whatever the issue is with the WiFi connection on the PC, it has generally not affected MythMote.

### Problem

I booted the machine one day and discovered that two recordings scheduled for the previous night had not occurred. Moreover, the front end was repeatedly telling me that the back end was off line ... even after I restarted the back end. Apparently the WiFi connection had flaked out (despite the network being up and the IP address being valid). With the MythTV box off line, the front end could not communicate with the back end, even though they're on the same machine.

### Solution

A DVR that cannot be depended upon to record is not much of a DVR, so the top priority was to eliminate the reliance on the uncertain WiFi connection. I switched the IP address for the back end to the localhost address (127.0.0.1). As long as the PC manages to wake up in time, the back end should (hypothetically) start and record.

The one problem with this change is that it effectively disconnects MythMote. The answer to that is port-forwarding, which I implemented as follows:
2. Edit the configuration file (/etc/rinetd.conf) to forward traffic on the static IP address to localhost. More specifically, I added the following forwarding rule (editing the file as root):

192.168.1.68 6546 127.0.0.1 6546

This forwards incoming traffic on port 6546 (the port used by the back end) at address 192.168.1.68 (the fixed IP address assigned to the MythTV machine in my LAN) to the same port on the local host address (where the back end is now listening).
3. The installer adds the rinet daemon to the set of programs that load automatically at boot. In my case, it showed up in /etc/rc1.d. Unfortunately, even though the daemon started, it failed to redirect MythMote traffic until it was restarted from a terminal. I suspect that it was loading before something else when it needed to load after that something else, though I have no idea what the something else was. My next step was to delete the line that automatically loads it at boot. On my box, this meant running

sudo rm /etc/rc1.d/K20rinetd

4. I then created a two-line script to manually run the daemon:
#!/bin/bash
gksudo /etc/init.d/rinetd restart
The specific name for the script (I used restart_rinetd.sh) and location are unimportant. I probably could have used the "start" command rather than the "restart" command, but this works (and maybe defends against the possibility that the daemon is already running but for some reason not connecting). I made the script executable with

chmod +x restart_rinetd.sh

5. Finally, I set the script up to start whenever I log in. Starting from the Applications menu (the main menu in Mythbuntu), I navigated to Applications > Settings > Session and Startup > Applications Autostart, clicked the Add button, typed in a rather arbitrary name and description, and used the file chooser to locate and select my new script file. After that, it was OK, Close and restart the machine to test it.

### Result

So far, at least, it works. When the machine boots up, I'm presented with a password input box. Whether I respond or not, the back end starts, so timed recordings should still work even if I'm not using the front end at recording time (and therefore not present to answer the password challenge). Once I supply my password (and sit through a small but harmless delay recognizing it), I'm into the front end, and MythMote is able to connect and function properly.

Update: That was stupid of me. The rinetd program can be executed by any user, not just root, so the use of gksudo (and ensuing password entry) was utterly pointless. I edited gksudo out of the script, and now startup works as it originally did: the back end and front end both start automatically, and I wind up in the front end without any intervention on my part.

Although I only have one front end (on the same machine), this should hypothetically allow someone to use the 127.0.0.1 address for the back end and still connect a remote front end, provided that they can figure out a way either to answer the password challenge or to get the script to run with root privileges without needing a password. One possibility (which I have not tested, since I don't have a remote front end) would be to have a script on the remote front end machine connect to the back end via ssh and start the daemon.


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# What Hermitian operators can be observables?

We can construct a Hermitian operator $O$ in the following general way:

1. find a complete set of projectors $P_\lambda$ which commute,
2. assign to each projector a unique real number $\lambda\in\mathbb R$.

By this, each projector defines an eigenspace of the operator $O$, and the corresponding eigenvalues are the real numbers $\lambda$. In the particular case in which the eigenvalues are non-degenerate, the operator $O$ has the form $$O=\sum_\lambda\lambda|\lambda\rangle\langle\lambda|$$

Question: what restrictions which prevent $O$ from being an observable are known?

For example, we can't admit as observables the Hermitian operators having as eigenstates superpositions forbidden by the superselection rules.

a) Where can I find an exhaustive list of the superselection rules?

b) Are there other rules?

Update:

c) Is the particular case when the Hilbert space is the tensor product of two Hilbert spaces (representing two quantum systems), special from this viewpoint?

-
A superselection rule is when no local operator can link between two states. It's exactly like when in statistical mechanics, you have zero probability of making a macroscopic motion. There is no exhaustive list, as any vaccum condensate which breaks an exact symmetry or makes a SUSY modulus is automatically a superselection sector maker. –  Ron Maimon May 8 '12 at 15:24

I think the fundamental object is quantum mechanics is not the Hilbert space and operators on it but the C*-algebra of observables. In this picture the Hilbert space appears as a representation of the algebra. Different irreducible representations are different superselection sectors. The answer to "which operator is observable" is thus simple: the observable operators are those that come from the algebra. Indeed its better to think of observables as self-adjoint elements of the algebra rather than as operators

You might ask where do we get the algebra from. Well, this already should be supplied by the particular model. For a quantum mechanical particle moving on a manifold $M$, the C*-algebra consists of all bounded operators on $L^2(\hat{M})$ commuting with $\pi_1(M)$ where $\hat{M}$ is the universal cover of $M$. The superselection sectors correspond to irreducible representations of $\pi_1(M)$. For QFTs the problem of constructing the algebra of observables is in general open however certain cases (such as free QFT and I believe rational CFT as well) were solved. An approach emphasizing the algebra point of view is Haag-Kastler axiomatic QFT

From the point of view of deformation quantization the quantum observable algebra is a non-commutative deformation of the algebra of continuous (say) functions on the classical phase space. This point of view is not fundamental but it's useful. For example it allows to understand different values of spin and different quantum statistics as superselection sectors

-
Thank you, this is very useful. –  Cristi Stoica Feb 14 '12 at 19:13
-1: This is useless. It doesn't answer the question, and is just a collection of impressive sounding trivial gibberish. You didn't say which observables could be measured, you defined "superselection sector" in the maximally unenlightening way, and your example of "different spin values" is wrong and the stuff you talk about is not useful. This is just terrible. –  Ron Maimon May 8 '12 at 15:19

Without superselection rules to restrict the observables, any Hermitian operator is an admissible observable. The case of multiple identical systems is very important. Indeed, if the systems are really identical, only observables that are symmetric under the exchange of the systems are admissible. In such a case, technically speaking you should only consider observables that commute with all possible permutation operators (i.e., with the elements of the representation of the permutation group on the Hilbert space of the systems).

-
Thank you for the answer. Indeed, for identical particles one takes as the Hilbert space as the quotient of the tensor product by the appropriate ideal. Do you know some bibliographic references showing that the only restrictions to a Hermitian operator to be observable are only these? –  Cristi Stoica Feb 14 '12 at 9:34
You can impose other superselection rules, typically based on some symmetry, not necessarily the exchange symmetry (that applies only for multi-particle systems). I cannot recommend a reference based on my direct knowledge, but I'd say you might start from rmp.aps.org/abstract/RMP/v79/i2/p555_1 –  Marco Feb 14 '12 at 18:51
Thank you, this helps. –  Cristi Stoica Feb 14 '12 at 19:15


text:
1. Jun 28, 2011

### hoomanya

Hi,
Just a simple, quick question:
Does the gradient of a vector give a scalor or a vector?
Thanks!

2. Jun 28, 2011

### tiny-tim

Last edited by a moderator: Apr 26, 2017
3. Jun 28, 2011

### hoomanya

4. Jun 28, 2011

### HallsofIvy

You can, of course, have
$$\nabla\cdot \vec{\phi}(x, y, z)= \frac{\partial f}{\partial x}+ \frac{\partial g}{\partial y}+ \frac{\partial h}{\partial z}$$
the "divergence" of the vector valued function, $\vec{\phi}(x, y, z)$, which is a scalar, or
$$\nabla\cdot \vec{\phi}= \left(\frac{\partial g}{\partial z}- \frac{\partial h}{\partial y}\right)\vec{i}+ \left(\frac{\partial f}{\partial z}- \frac{\partial h}{\partial x}\right)\vec{j}+ \left(\frac{\partial g}{\partial x}- \frac{\partial f}{\partial y}\right)\vec{i}$$
the "curl" of the vector valued function, $\vec{\phi}(x, y, z)$, which is a vector.

Perhaps that is what you are thinking of. There are three kinds of vector "multiplication" and so three ways we can attach the "del" operator to a function.

5. Jun 28, 2011

### qbert

I'd say there's a perfectly good definition for the gradient of a vector.
it's a rank-2 cartesian tensor.

For the vector $$\vec{A} = A_x \hat{i} + A_y \hat{j} + A_z \hat{k}$$

we have the beast $$\nabla \vec{A} =\nabla A_x \hat{i} + \nabla A_y \hat{j} + \nabla A_z \hat{k}$$

such that for any vector $\vec{v}$
$$\vec{v} \cdot \nabla \vec{A} = (\vec{v} \cdot \nabla A_x) \hat{i} + (\vec{v} \cdot \nabla A_y) \hat{j} + (\vec{v} \cdot \nabla A_z) \hat{k}$$

This is more clear in component notation
$$\vec{A} \rightarrow A^i$$
then
$$\nabla \vec{A} \rightarrow (\nabla A)^i_j = \frac{\partial A^i}{\partial x^j}.$$

where the product with the vector $\vec{v}$ above is really
contraction on the second index.
$$\vec{v} \cdot \nabla \vec{A} \rightarrow \sum_j \quad \left( v^j \frac{\partial A^i}{\partial x^j} \right)$$


text:
## Baccelli and Mongin (and others) on redescribing the outcomes

There are many alleged counterexamples to expected utility theory: Allais's Paradox, Ellsberg's Paradox, Sen (1993)'s polite agent who prefers the second-largest slice of cake, Machina (1989)'s mother who prefers fairness when giving a treat to her children, and so on. In all these cases, the preferences of seemingly reasonable people appear not to rank the options by their expected utility.

Those who make these claims generally assume that utility is a function of material goods. In Allais's Paradox, for example, the possible "outcomes" (of which utility is a function) are assumed to be amounts of money. As has often been pointed out, the apparent violations of expected utility theory all go away if the outcomes are individuated more finely – if, for example, we distinguish between an outcome of getting $1000 as the result of a risky gamble and an outcome of getting a sure$1000. See, for example, Weirich (1986), or Dreier (1996).

The view that many apparent counterexamples to the expected utility model can be explained away by redescribing the outcomes is common in philosophy, but very uncommon everywhere else.

I think the disagreement is largely verbal. The two camps are interested in different topics, and they mean different things by 'utility'.

Economists would like to establish certain regularities in consumer behaviour that allow deriving laws of supply, demand, variable proportion, etc. One can derive such laws if one assumes that people assign a certain "utility" to material goods – irrespective of whether the goods are already owned, how they are acquired, and so on – and that their choices maximize the expectation of this "utility" function. (According to the revealed preference doctrine, this assumption is equivalent to assuming that people have preferences over lotteries (or gambles) involving material goods that conform to certain axioms.)

In fact, of course, people don't just care about material goods. We care about politeness, safety, fairness, predictability, feelings of excitement or regret, and so on. Hence the apparent counterexamples to "expected utility theory".

When we philosophers talk about expected utility, we are (for the most part) interested in a high-level, general theory about how one should act in order to promote some goals in light of some information, without putting substantive constraints on the relevant goals. When we talk about an agent's utility function, we assume that the function represents everything the agent ultimately cares about. Utility, on this usage, isn't a function of material goods.

Our expected utility model is much weaker than the economists' model. On its own, it doesn't make any predictions about consumer behaviour, or about any other kind of behaviour. Any behaviour whatsoever can be made to conform to the philosophical EU model. This is as it should be. For any behaviour, one can imagine an agent whose only goal is to display just that behaviour. Displaying the behaviour is surely a good way of promoting the goal.

Some, however, have argued that it is wrong to redescribe the outcomes. Lara Buchak argues against what she calls "global redescriptions" in chapter 4 of Buchak (2013). Jean Baccelli and Phillippe Mongin argue against all kinds of redescription in Mongin and Baccelli (2020) and Baccelli and Mongin (2021).

Buchak and Baccelli and Mongin all complain that unconstrained redescription would trivialise the expected utility model. In this context, they discuss some proposed limits on allowable redescriptions.

Broome (1991, 103), for example, suggests that "outcomes should be distinguished as different iff they differ in a way that makes it rational to have a preference between them". Gustafsson (2022, 14) similarly suggests that "outcomes x and y should be treated as the same if and only if it is rationally required to be indifferent between the sure prospects of x and y".

I disagree.

Suppose we judge that rationality requires indifference between x and y. We can nonetheless imagine an agent who (irrationally) prefers x to y. When given a straight choice between x and y, the agent would choose x. She would pay to get x rather than y. And so on. According to Broome and Gustaffson, this person's utility function assigns the same value to x and y, simply because utility functions are defined so that they can't distinguish between x and y. According to Broome and Gustaffson, our agent violates the expected utility norm when she chooses x over y.

I don't think this is a useful description of the scenario. Our agent isn't acting against her desires. She does exactly what she ought to do in light of her desire for x over y. What we should say is that she assigns greater utility to y than to x, that her choice of x is in line with the EU norm, but that her desire for y is irrational.

So I don't think we should put any non-trivial constraints on redescriptions.

Baccelli and Mongin complain that this makes the redescription strategy ad hoc and unsystematic. But this isn't true.

Every systematic EU model should have something to say about how the "outcomes" are individuated. One attractive idea, adopted for example in Lewis (1981), is to identify outcomes with "value-level propositions", assuming the theory of value developed in Jeffrey (1965). Another natural idea, popular in ethics, is that outcomes are complete worlds: the outcome of an act in a particular decision situation comprises everything that would be the case if the act were chosen.

Either way, it is guaranteed that an outcome specifies everything that matters to the agent, even if the agent has unreasonable goals. By contrast, it is really not obvious at all why one might think that merely specifying material goods is a useful representation of an outcome.

We shouldn't assume that the material-goods individuation is somehow correct by default, and that everyone else is "redescribing".

Baccelli and Mongin also complain that the redescription strategy is "theoretically insulated" from non-EU models that are tailored to specific violations of standard EU theory, as understood outside philosophy. Some such models specifically allow an agent to care about politeness. Others allow agents to care about regret. Others allow them to care about "ambiguity". One might add Buchak's "risk-weighted EU theory" that allows agents to care about risk (in a highly constrained manner).

As a philosopher who is interested in the EU model as a general model of the connection between goals, beliefs, and behaviour, I really don't take much interest in these developments. All these models are far too restrictive in what kinds of goals they allow for.

But that's the point. I'm interested in a different topic. I don't want to derive the law of demand from a predictively powerful model of consumer behaviour.

If this were my topic, I think I would try to develop models that keep the simple EU rule and instead constrain the utility function. Pettigrew (2015) shows how Buchak's model can be re-phrased in this manner. Mongin and Baccelli (2020) say that it would be "utterly unpractical" to develop models of regret along these lines. Perhaps they are right. Perhaps it really proves more convenient, for some applications, to stick with a "utility" function that's only defined over material goods and revise the EU rule.

It's unfortunate that the same labels – 'decision theory', 'expected utility theory' – are used for these different projects.

Baccelli, Jean, and Philippe Mongin. 2021. “Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory?” Philosophical Studies. doi.org/10.1007/s11098-021-01723-z.
Broome, John. 1991. Weighing Goods. Oxford: Blackwell.
Buchak, Lara. 2013. Risk and Rationality. Oxford: Oxford University Press.
Dreier, James. 1996. “Rational Preference: Decision Theory as a Theory of Practical Rationality.” Theory and Decision 40 (3): 249–76. doi.org/10.1007/BF00134210.
Gustafsson, Johan E. 2022. “Money-Pump Arguments.” Elements in Decision Theory and Philosophy. doi.org/10.1017/9781108754750.
Jeffrey, Richard. 1965. The Logic of Decision. New York: McGraw-Hill.
Lewis, David. 1981. “Causal Decision Theory.” Australasian Journal of Philosophy 59: 5–30.
Machina, Mark J. 1989. “Dynamic Consistency and Non-Expected Utility Models of Choice Under Uncertainty.” Journal of Economic Literature 27 (4): 1622–68.
Mongin, Philippe, and Jean Baccelli. 2020. “Expected Utility Theory, Jeffrey’s Decision Theory, and the Paradoxes.” Synthese. doi.org/10.1007/s11229-020-02691-3.
Pettigrew, Richard. 2015. “Risk, Rationality and Expected Utility Theory.” Canadian Journal of Philosophy 45 (5-6): 798–826. doi.org/10.1080/00455091.2015.1119610.
Sen, Amartya. 1993. “Internal Consistency of Choice.” Econometrica 61 (3): 495–521. doi.org/10.2307/2951715.
Weirich, Paul. 1986. “Expected Utility and Risk.” The British Journal for the Philosophy of Science 37 (4): 419–42.


text:
# American Institute of Mathematical Sciences

• Previous Article
Approximate models for stochastic dynamic systems with velocities on the sphere and associated Fokker--Planck equations
• KRM Home
• This Issue
• Next Article
A kinetic approach to error estimate for nonautonomous anisotropic degenerate parabolic-hyperbolic equations
September  2014, 7(3): 493-507. doi: 10.3934/krm.2014.7.493

## Hysteretic behavior of a moment-closure approximation for FENE model

 1 Division of Mathematical Models, National Institute for Mathematical Sciences, Daejeon, 305-811, South Korea

Received  February 2014 Revised  May 2014 Published  July 2014

We discuss hysteretic behaviors of dilute viscoelastic polymeric fluids with moment-closure approximation approach in extensional/enlongational flows. Polymeric fluids are modeled by the finite extensible nonlinear elastic (FENE) spring dumbbell model. Hysteresis is one of key features to describe FENE model. We here investigate the hysteretic behavior of FENE-D model introduced in [Y. Hyon et al., Multiscale Model. Simul., 7(2008), pp.978--1002]. The FENE-D model is established from a special equilibrium solution of the Fokker-Planck equation to catch extreme behavior of FENE model in large extensional flow rates. Since the hysteresis of FENE model can be seen during a relaxation in simple extensional flow employing the normal stress/the elongational viscosity versus the mean-square extension, we simulate FENE-D in simple extensional flows to investigate its hysteretic behavior comparing to FENE-P, FENE-L [G. Lielens et al., J. Non-Newtonian Fluid Mech., 76(1999), pp.249--279]. The FENE-P is a well-known pre-averaged approximated model, and it shows a good agreement to macroscopic induced stresses. However, FENE-P does not catch any hysteretic phenomenon. In contrast, the FENE-L shows a better hysteretic behavior than the other models to FENE, but it has a limitation for macroscopic induced stresses in large shear rates. On the other hand, FENE-D presents a good agreement to macroscopic induced stresses even in large shear rates, and moreover, it shows a hysteretic phenomenon in certain large flow rates.
Citation: YunKyong Hyon. Hysteretic behavior of a moment-closure approximation for FENE model. Kinetic and Related Models, 2014, 7 (3) : 493-507. doi: 10.3934/krm.2014.7.493
##### References:
 [1] R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1, Fluid Mechanics, John Wiley & Sons, New York, 1977. [2] R. B. Bird, O. Hassager, R. C. Armstrong and C. F. Curtiss, Dynamics of Polymeric Fluids, Vol. 2, Kinetic Theory, John Wiley & Sons, New York, 1977. [3] C. Chauviere and A. Lozinski, Simulation of dilute polymer solutions using a Fokker-Planck equation, Computers & fluids, 33 (2004), 687-696. doi: 10.1016/j.compfluid.2003.02.002. [4] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford, UK, 1986. [5] P. S. Doyle, E. S. G. Shaqfeh, G. H. McKinley and S. H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech., 76 (1998), 79-110. doi: 10.1016/S0377-0257(97)00113-4. [6] Q. Du, C. Liu and P. Yu, FENE Dumbbell model and its several linear and nonlinear closure approximations, Multiscale Model. Simul., 4 (2005), 709-731. doi: 10.1137/040612038. [7] M. Gurtin, An Introduction to Continuum Mechanics, Academic Press, New York, 1981. [8] M. Herrchen and H. C. Öttinger, A detail comparison of various FENE dumbbell models, J. Non-Newtonian Fluid Mech., 68 (1997), 17-42. doi: 10.1016/S0377-0257(96)01498-X. [9] Y. Hyon, Q. Du and C. Liu, An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials, Multiscale Model. Simul., 7 (2008), 978-1002. doi: 10.1137/070708287. [10] M. Hulsen, A. van Heel and B. van dent Brule, Simulation of viscoelatsic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech., 70 (1997), 79-101. [11] B. Jourdain, C. Le Bris and T. Lelievre, On a variance reduction technique for the micro-macro simulations of polymeric fluids, J. Non-Newtonian Fluid Mech., 122 (2004), 91-106. doi: 10.1016/j.jnnfm.2003.09.006. [12] B. Jourdain, T. Lelievre and C. Le Bris, Existence of solution for a micro-macro model of polymeric fluid: The FENE model, J. Funct. Anal., 209 (2004), 162-193. doi: 10.1016/S0022-1236(03)00183-6. [13] R. Keunings, On the Peterlin approximation for finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 68 (1997), 85-100. doi: 10.1016/S0377-0257(96)01497-8. [14] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. doi: 10.1007/978-3-662-12616-5. [15] M. Laso and H. C. Ottinger, Calculation of viscoelastic flow using molecular models: The connffessit approach, J. Non-Newtonian Fluid Mech., 47 (1993), 1-20. doi: 10.1016/0377-0257(93)80042-A. [16] G. Lielens, P. Halin, I. Jaumain, R. Keunings and V. Legat, New closure approximations for the kinetic theory of finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 76 (1998), 249-279. doi: 10.1016/S0377-0257(97)00121-3. [17] G. Lielens, R. Keunings and V. Legat, The FENE-L and FENE-LS closure approximations to the kinetic theory of finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 87 (1999), 179-196. doi: 10.1016/S0377-0257(99)00063-4. [18] F. H. Lin, C. Liu and P. Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math., 60 (2007), 838-866. doi: 10.1002/cpa.20159. [19] H. C. Öttinger, Stochastic Processes in Polymeric Fluids, Tools and Examples for Developing Simulation Algorithms, Springer-Verlag, Berlin, 1996. doi: 10.1007/978-3-642-58290-5. [20] R. Owens and T. Phillips, Computational Rheology, Imperial College Press, London, 2002. doi: 10.1142/9781860949425. [21] R. Prabhakar and J. R. Prakash, Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction, J. Rheol., 50 (2006), 561-593. doi: 10.1122/1.2206715. [22] R. Sizaire, G. Lielens, I. Jaumain, R. Keunings and V. Legat, On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow, J. Non-Newtonian Fluid Mech., 82 (1999), 233-253. doi: 10.1016/S0377-0257(98)00164-5. [23] H. Wang, K. Li and P. Zhang, Crucial properties of the moment closure model FENE-QE, J. Non-Newtonian Fluid Mech., 150 (2008), 80-92. doi: 10.1016/j.jnnfm.2007.10.013. [24] P. Yu, Q. Du and C. Liu, From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids, Multiscale Model. Simul., 3 (2005), 895-917. doi: 10.1137/030602794.

show all references

##### References:
 [1] R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1, Fluid Mechanics, John Wiley & Sons, New York, 1977. [2] R. B. Bird, O. Hassager, R. C. Armstrong and C. F. Curtiss, Dynamics of Polymeric Fluids, Vol. 2, Kinetic Theory, John Wiley & Sons, New York, 1977. [3] C. Chauviere and A. Lozinski, Simulation of dilute polymer solutions using a Fokker-Planck equation, Computers & fluids, 33 (2004), 687-696. doi: 10.1016/j.compfluid.2003.02.002. [4] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Clarendon Press, Oxford, UK, 1986. [5] P. S. Doyle, E. S. G. Shaqfeh, G. H. McKinley and S. H. Spiegelberg, Relaxation of dilute polymer solutions following extensional flow, J. Non-Newtonian Fluid Mech., 76 (1998), 79-110. doi: 10.1016/S0377-0257(97)00113-4. [6] Q. Du, C. Liu and P. Yu, FENE Dumbbell model and its several linear and nonlinear closure approximations, Multiscale Model. Simul., 4 (2005), 709-731. doi: 10.1137/040612038. [7] M. Gurtin, An Introduction to Continuum Mechanics, Academic Press, New York, 1981. [8] M. Herrchen and H. C. Öttinger, A detail comparison of various FENE dumbbell models, J. Non-Newtonian Fluid Mech., 68 (1997), 17-42. doi: 10.1016/S0377-0257(96)01498-X. [9] Y. Hyon, Q. Du and C. Liu, An enhanced macroscopic closure approximation to the micro-macro FENE model for polymeric materials, Multiscale Model. Simul., 7 (2008), 978-1002. doi: 10.1137/070708287. [10] M. Hulsen, A. van Heel and B. van dent Brule, Simulation of viscoelatsic flow using Brownian configuration fields, J. Non-Newtonian Fluid Mech., 70 (1997), 79-101. [11] B. Jourdain, C. Le Bris and T. Lelievre, On a variance reduction technique for the micro-macro simulations of polymeric fluids, J. Non-Newtonian Fluid Mech., 122 (2004), 91-106. doi: 10.1016/j.jnnfm.2003.09.006. [12] B. Jourdain, T. Lelievre and C. Le Bris, Existence of solution for a micro-macro model of polymeric fluid: The FENE model, J. Funct. Anal., 209 (2004), 162-193. doi: 10.1016/S0022-1236(03)00183-6. [13] R. Keunings, On the Peterlin approximation for finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 68 (1997), 85-100. doi: 10.1016/S0377-0257(96)01497-8. [14] P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992. doi: 10.1007/978-3-662-12616-5. [15] M. Laso and H. C. Ottinger, Calculation of viscoelastic flow using molecular models: The connffessit approach, J. Non-Newtonian Fluid Mech., 47 (1993), 1-20. doi: 10.1016/0377-0257(93)80042-A. [16] G. Lielens, P. Halin, I. Jaumain, R. Keunings and V. Legat, New closure approximations for the kinetic theory of finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 76 (1998), 249-279. doi: 10.1016/S0377-0257(97)00121-3. [17] G. Lielens, R. Keunings and V. Legat, The FENE-L and FENE-LS closure approximations to the kinetic theory of finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., 87 (1999), 179-196. doi: 10.1016/S0377-0257(99)00063-4. [18] F. H. Lin, C. Liu and P. Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math., 60 (2007), 838-866. doi: 10.1002/cpa.20159. [19] H. C. Öttinger, Stochastic Processes in Polymeric Fluids, Tools and Examples for Developing Simulation Algorithms, Springer-Verlag, Berlin, 1996. doi: 10.1007/978-3-642-58290-5. [20] R. Owens and T. Phillips, Computational Rheology, Imperial College Press, London, 2002. doi: 10.1142/9781860949425. [21] R. Prabhakar and J. R. Prakash, Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction, J. Rheol., 50 (2006), 561-593. doi: 10.1122/1.2206715. [22] R. Sizaire, G. Lielens, I. Jaumain, R. Keunings and V. Legat, On the hysteretic behaviour of dilute polymer solutions in relaxation following extensional flow, J. Non-Newtonian Fluid Mech., 82 (1999), 233-253. doi: 10.1016/S0377-0257(98)00164-5. [23] H. Wang, K. Li and P. Zhang, Crucial properties of the moment closure model FENE-QE, J. Non-Newtonian Fluid Mech., 150 (2008), 80-92. doi: 10.1016/j.jnnfm.2007.10.013. [24] P. Yu, Q. Du and C. Liu, From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids, Multiscale Model. Simul., 3 (2005), 895-917. doi: 10.1137/030602794.
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text:
# Counterexample Math Books

I have been able to find several counterexample books in some math areas. For example:

$\bullet$ Counterexamples in Analysis, Bernard R. Gelbaum, John M. H. Olmsted

$\bullet$ Counterexamples in Topology, Lynn Arthur Steen, J. Arthur Seebach Jr.

$\bullet$ Counterexamples in Probability and Statistics, Joseph P. Romano, A.F. Siegel

$\bullet$ Counterexamples in Probability and Real Analysis, Gary L. Wise and Eric B. Hall

$\bullet$ Counterexamples in Probability, Jordan M. Stoyanov

Why are there no other examples of books in other math topics (number theory, numerical analysis, DEQs, PDEs, Dynamical Systems, Discrete Math...)?

Is it that it is just not a rich enough area, examples are too trivial, the book wouldn't warrant publishing (low sales), someone just hasn't written one, I missed it or something else?

Regards

• Your list is not complete. – Michael Greinecker Jan 15 '13 at 16:16
• Nice question! Maybe, community wiki fits it? – Ilya Jan 15 '13 at 16:16
• Great idea...I wish we'd have the opportunity to collect lists, even if Community Wiki, that people can update, modify, add...for many topics! +1 – Namaste May 21 '13 at 0:14
• nice question !!! – user111750 Mar 11 '15 at 6:44

The following list of titles, all of which can be found on Amazon, may help to answer the question:

• Counterexamples in Optimal Control Theory

• Lectures on Counterexamples in Several Complex Variables

• Counterexamples in Topological Vector Spaces

• Theorems and Counterexamples in Mathematics

• Counterexamples in Calculus

• Convex Functions: Constructions, Characterizations and Counterexamples

• Surprises and Counterexamples in Real Function Theory

• Examples and Counterexamples in Graph Theory

• Counter-Examples In Differential Equations And Related Topics

• @michealGreinecker these books are very much addictive. It is a different kind of fun to read them. Please add a few more – Kislay Tripathi Oct 15 '17 at 11:56
• Steen, L. A.; Seebach, J. A. jun., Counterexamples in topology, New York etc.: Holt, Rinehart and Winston, Inc., XIII, 210 p. (1970). ZBL0211.54401.

• Gelbaum, B. R.; Olmsted, J. M. H., Counterexamples in analysis, Moskau: Verlag ’Mir’ 251 S. (1967). ZBL0156.05801.

• Stoyanov, Jordan M., Counterexamples in probability, Wiley Series in Probability and Mathematical Statistics. Chichester etc.: John Wiley & Sons. XXIII, 313 p.; \textsterling 38.50 (1987). ZBL0629.60001.

• All three of these books are mentioned in the original question... – Xander Henderson Sep 17 at 14:58
• thanks. I followed a link directing me to the answer by Michael above directly so I overlooked the original post. – ALife Sep 18 at 14:35


text:
# How to Calculate Radius?

Radius is the distance from the center of the circle to the edge. To calculate the radius you can do it from a known diameter divided by two or divide the area by pie.
How to Calculate Radius
The radius is the distance from the center of a circle to its edge and is a necessary measure in calculating other dimensions. For example, the area of a circle is the radius squared times the value of Pi (3.1416), and the volume of a sphere is... More »
Difficulty: Moderately Easy
Source: www.ehow.com
Q&A Related to "How to Calculate Radius?"
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 1. Measure without any other measurement. Draw a square around the circle. All sides of the square must touch the circle (be tangential) Measure the length of any 1 side of the square http://www.wikihow.com/Calculate-the-Radius-of-a-C...
 See the book. The Effects of Nuclear Weapons. for equations. My copy came with a circular slide rule that calculates that for optimal altitude airburst and surface burst over a yield http://wiki.answers.com/Q/How_is_a_blast_radius_ca...
 Use the formula to find the radius of a body from its gravitational http://www.chacha.com/question/how-to-calculate-th...
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The radius of gyration which is also known as gyradius is the related measures of the size of an object or surface. It is calculated by getting the root mean square ...
To calculate turning radius, start by getting the equation. Find the number for WB in the equation. WB stands for wheel base. Find the number for OWC in the equation ...
To calculate turning radius you use the equation CCR (feet) = WB (inches) times CF/OWC (degrees). CCR stands for curb-to-curb turning radius. WB is the wheelbase ...
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text:
# 7 Regularization

## The Problem of Overfitting

Regularization, that will allow us to ameliorate or to reduce this overfitting problem and get these learning algorithms to maybe work much better.

If you were to fit a very high-order polynomial, if you were to generate lots of high-order polynomial terms of speeches, then, logistical regression may contort itself, may try really hard to find a decision boundary that fits your training data or go to great lengths to contort itself, to fit every single training example well.
But this really doesn’t look like a very good hypothesis, for making predictions.

The term generalized refers to how well a hypothesis applies even to new examples.

In order to address over fitting, there are two main options for things that we can do.

• reduce the number of features
• regularization, keep all the features, but we’re going to reduce the magnitude or the values of the parameters
• ## Cost Function

#### Orignal Model :

$$h_\theta(x) = \theta_0 + \theta_1x_1 + \theta_2x\underset{2}{2} + \theta_3x\underset{3}{3} + \theta_4x\underset{4}{4}$$

#### Modified Model :

$$\underset{\theta }{min}\frac{1}{2m}[\sum_{i=1}^{m}(h_\theta(x^{(i)}-y^{(i)})^2+1000\theta\underset{3}{2}+10000\theta \underset{4}{2})]$$

#### Suppose :

$$J(\theta) = \frac {1}{2m} [\sum_{i=1}^{m} (h_\theta(x^{(i)}-y^{(i)})^2 + \lambda \sum_{j=1}^{n} \theta _j^2]$$

regularization parameter : $$\lambda$$

#### Notice :

$$\lambda \sum_{j=1}^{n} \theta _j^2$$

The extra regularization term at the end to shrink every single parameter and so this term we tend to shrink all of my parameters.

## Regularized Linear Regression

$$J(\theta) = \frac {1}{2m} [\sum_{i=1}^{m} (h_\theta(x^{(i)}-y^{(i)})^2 + \lambda \sum_{j=1}^{n} \theta _j^2]$$

repeat until convergence {

$$\theta _0 := \theta _0 – \alpha \frac {1}{m} \sum _{i=1}^{m} (h_\theta (x^{(i)}) – y^{(i)})x_0^{(i)}$$
$$\theta _j := \theta _j – \alpha [\frac {1}{m} \sum _{i=1}^{m} (h_\theta (x^{(i)}) – y^{(i)})x_j^{(i)} + \frac {\lambda }{m}\theta _j]$$

}

#### Modified :

$$\theta _j := \theta _j(1 – \alpha \frac {\lambda }{m}) – \alpha \frac {1}{m} \sum _{i=1}^{m} (h_\theta (x^{(i)}) – y^{(i)})x_j^{(i)}$$

## Regularized Logistic Regression

$$J(\theta) = \frac {1}{m}\sum _{i=1}^{m} [-y^{(i)} log(h_\theta (x^{(i)})) – (1 – y^{(i)})log(1 – h_\theta (x^{(i)}))] + \frac {\lambda}{2m} \sum _{i=1}^{n} \theta _j^{2}$$

#### Python Code :

1. import numpy as np
2. def costReg(theta, X, y, learningRate):
3. 	theta = np.matrix(theta)
4. 	X = np.matrix(X)
5. 	y = np.matrix(y)
6. 	first = np.multiply(-y, np.log(sigmoid(X * theta.T)))
7. 	second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T)))
8. 	reg = learningRate / (2 * len(X)) * np.sum(np.power(theta[:,1:theta.shape[1]], 2))
9. 	return np.sum(first - second) / len(X) + reg


text:
Algebra 1: Common Core (15th Edition)

You have the sequence:6,-12,24,-48. Find the common ratio by using the formula: R=$\frac{a2}{a1}$,R=$\frac{a4}{a3}$.Plug in the values to get the ratios. r=$\frac{-12}{6}$=-2 r=$\frac{-48}{24}$=-2 There is a common ratio, r=-2. So the sequence is geometric.