Does an equivalent of ArcScripts exist?  I know of the the ArcGIS resource center and "Code Galleries" but does something that equates to ArcScripts where users share useful ArcGIS code exist? The new ArcGIS forums are not great for searching for code either.  It seems to me as through the ESRI replacement for ArcScripts are a poor replacement and I am wondering if something 3rd party exists.  I know we can still search ArcScripts but it does not appear to still be an active repository.
I will be writing scripts for ArcGIS Desktop in Python with ArcPy.   Is there a community or open source project where code and models can be shared?
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$   Here's what I did so far:  Let $\sup A, \sup B$, and $\sup (A \cup B)$ denote upper bounds of $A,B$, and $A \cup B$, respectively. If $x \in A$, then $x \le \sup A$. If $x \in B$, then $x \le \sup B$. In either case, $x \in (A \cup B)$. So either $x \le \sup A$ or $x \le \sup B$. In either case, $x \le \max \{\sup A, \sup B\}$. So $\max \{\sup A, \sup B\}$ is the upper bound of $A \cup B$, which means $\sup (A \cup B) \le \max\{\sup A, \sup B\}$.  I do not know if there's a better way to go at it, but all I did was show the inequality. Can I do this, and show the reverse inequality? If so, how can I go about doing that? I want to subtract the current frame from a previous frame, I have a image sequence and I want blender to subtract the current frame from the frame with an offset of -4. If I am on frame 5 so blender will subtract and use frame 1. Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? I think the answer is yes.   Sketch of the proof Consider $\mathbb{R}$ as a vector space over $\mathbb{Q}$. Let $\{e_\lambda:\lambda\in\Lambda\}\subset\mathbb{R}$ be its Hamel basis. Then $\{(e_{\lambda_1},e_{\lambda_2}):\lambda_1,\lambda_2\in\Lambda\}\subset\mathbb{R}^2$ is a Hamel basis of $\mathbb{R}^2$. Consider set theoretic bijection $i:\Lambda\to\Lambda\times\Lambda$ define map $\varphi:\mathbb{R}\to\mathbb{R}^2$ by its action on element of Hamel basis of $\mathbb{R}$ by equality $\varphi(e_\lambda)=(e_{i(\lambda)_1},e_{i(\lambda)_2})$. This is an isomorphism between $\mathbb{Q}$-vector spaces $\mathbb{R}$ and $\mathbb{R}^2$.  Question Could you tell me is this proof correct, and if it is not, where is the mistake?  EDIT: Thanks to GAJO we found that this proof is wrong. The correct one basis is  $$ \{(e_\lambda,0):\lambda\in \Lambda\}\cup\{(0,e_\lambda):\lambda\in\Lambda\} $$ So we had to look at bijections of the form $i:\Lambda\to\Lambda\coprod\Lambda$ and the desired linear operator is defined by equalities $\varphi(e_\lambda)=(e_{i(\lambda)},0)$ if $i(\lambda)$ lies in the first copy $\Lambda$ and $\varphi(e_\lambda)=(0,e_{i(\lambda)})$ otherwise. What's the best way to write Mathematical Equations on the Web? How do I make the Super key open the activities overview in Ubuntu 20.04 LTS? Can you help me with this inequality?  $|x-1| +|x+1| &lt;1$.  I think that it doesn't exist an $x$ that satisfies this inequality, but I'm not really convinced about my answer. I was doing graph theory homework. I was counting the spaning trees of graph G. Such that G is two complete graphs on n vertices connected by two edges. I got to this expression: $$2n^{2\left(n-2\right)}+2\left(n^{\left(n-2\right)}\sum_{i=0}^{n-2}\binom{n-2}{i}\left(1+i\right)^{\left(i-1\right)}\left(n-i-1\right)^{\left(n-i-3\right)}\right)$$ I know that this expression gives the correct result, however, I was told by my teacher that it is possible to express that number in closed form e.g. without the summation. However, I have yet to find a solution. Beamer: change header background color I have decided to switch from Powerpoint to Beamer, and for my first presentation I'd like to use the , and the same colors as in this goggle slide template:  .  I tried to do some research about it, the closest answers I found are the question  and the . I tried this code:  \documentclass{beamer} \usepackage[frenchb]{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}  \usetheme{metropolis}  \definecolor{bluegreen}{rgb}{3, 166, 155} \definecolor{pitchblack}{rgb}{0, 0, 0} \definecolor{lightbeige}{rgb}{255, 251, 241} \definecolor{mediumgray}{rgb}{183, 183, 183}  \setbeamercolor{background canvas}{bg=pitchblack} \setbeamercolor{normal text}{fg=lightbeige} \setbeamercolor{headline}{bg=bluegreen, fg=mediumgray}  \begin{document} \begin{frame}     \frametitle{The title}     Lorem ipsum... \end{frame} \end{document}   I does everything I want, except that the title bar's background color is lightbeige:    What did I do wrong? Or what argument should I pass to \setbeamercolor to get it right? Thanks in advance :-). I'm doing some architectural cleanup that involves moving a bunch of classes into different projects and/or namespaces. Currently I'm moving the files by hand, building, and then manually adding using Foo statements as needed to resolve compilation errors. Anyone know of a smarter way of doing this? (We're a CodeRush and Refactor! shop, but I'd be interested to hear if Resharper has support for this) Applying for a UK Tourist Visa from outside country of origin Given a fraction:  $$\frac{a}{b}$$  I now add a number $n$ to both numerator and denominator in the following fashion:  $$\frac{a+n}{b+n}$$  The basic property is that the second fraction is suppose to closer to $1$ than the first one. My question is how can we prove that?  What I have tried:  I know $\frac{n}{n} = 1$ so now adding numbers $a$ and $b$ to it would actually "move it away" from $1$. But I cannot understand why $\frac{a}{b}$ is actually farther away from $1$ than $\frac{a+n}{b+n}$.  Why is that? What does it mean to add a number to both the numerator and denominator? Trigger to use HTTP callout and update record with the results I have been trying to integrate Google Shortener API into my salesforce org. I wrote a class to make the call out, but am having difficulty bringing the value back into the record. I have a custom object called "referral_advocate__c" with a field called "Short_URL__c". Anytime the field "unique_ID__c" has a value, I am wanting to send this value with a static URL to google shortener and then save the response value to "referral_advocate__c.short_URL__c" on the record. This is the class to make the call out:  public class URLshort {  final string urls = 'https://www.myurl.com'; referral_advocate__c adv = new referral_advocate__c();  @future(callout = true) public static void URLshortner() {      HttpRequest req = new HttpRequest();     HttpResponse res = new HttpResponse();     Http http = new Http();      req.setEndpoint('https://www.googleapis.com/urlshortener/v1/url?key=myapikey');     req.setMethod('POST');     req.setHeader('Content-Type','application/json');            req.setBody('{"longUrl":+urls + adv.unique_reference_number_c}');       try {         res = http.send(req);         System.debug(res.getBody());     } catch(System.CalloutException e) {         System.debug('Callout error: '+ e);         System.debug(res.toString());     }   }  }   The after insert trigger on "referral_advocate__c" I wrote is not firing correctly. How do I return the results from this class and update the field "short_URL__C" with the returned value from a trigger? RMSE vs Standard deviation in population Capitalization of the word "the" in "the Lord" / "The Lord" Should I capitalize the word "the" when speaking of God as "the/The Lord"?     I praise the Lord.   or...     I praise The Lord. What is meant by "Constant Amortized Time" when talking about time complexity of an algorithm? Conjugacy classes in $A_n$. Suppose $n$ is a non negative integer $\geq 4$ and $\sigma\in S_n$ a permutation. Conjugacy classes in $S_n$ are completley determined by the cycle structure of $\sigma$. If we let the alternating group $A_n$.act on $S_n$ by conjugation, the orbits coincide with the conjugacy classes in $S_n$ except for those (even) permutations whose cycle structure is composed of even cycles (which corresponds to cycles of uneven length) of distinct order (fixed points are treated as cycles of length $1$.) See   For instance a $3$-cycle in $A_4$ has cycle structure $[3,1]$ which fits the bill, and a $5$-cycle in $A_5$ or $A_6$ works too, since the cycle structure is $[5]$ and $[5,1]$ respectively. On the other hand, a $3$-cycle in $A_5$ will does not satisfy the criteria as it has cycle structure $[3,1,1]$ with two fixed points.  In this case, the conjugacy class of $\sigma$ inside $S_n$ splits in $2$ orbits of the conjugation action of $A_n$, and if $\tau$ is any odd permutation, for instance $(12)$, then we have $$\mathrm{Conj}_{S_n}(\sigma)=\mathcal{O}(\sigma)\coprod\mathcal{O}(\tau\sigma\tau^{-1})$$  My question is How can we differentiate between the two orbits? Does it have geometric meaning?    I can see that this information can be useful when looking at representations of the alternating groups, since there are as many irreducible representations as conjugacy classes. As for some geometric interpretation, I ask because there is one for the three cycles in $A_4$. If $S_4$ is understood as the group of symmetries of a regular tetrahedron, then $A_4$ is the subgroup of direct symmetries, and a $3$-cycle corresponds to a rotation of angle $\frac{2\pi}{3}$ or $\frac{4\pi}{3}$ with axis passing through one of the vertices. Conjugacy classes inside $A_n$ preserve the angle, and that's how we can tell them apart. In this case the computations are so simple we don't really need this picture, but I think it is a nice way to understand the fact $3$-cycles in are not all conjugate inside $A_4$... The origin of the value of speed of light in vacuum Sending multiple messages through only one SocketChannel If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess). I have a land cover classification derived from Landsat TM imagery - I created this classification using ENVI. I would like to edit individual and groups of cells in some areas of the classification in order to improve the accuracy of the output by comparing it with aerial imagery.  Is there a way, using ArcGIS Desktop, to manually edit large groups of cells by selecting them and assigning them to a new or existing class?   I am aware of merging methods based on class statistics, but the area I'm classifying has a high amount of spectral confusion due to thin cloud cover - it seems like a manual edit is the only way to go.