ArcScene3D layer rendering problem
How to properly Drape vectors over a DEM?
A reflection question about a complex function My question is how would I go about proving this?     Prove that $R$ is a local ring if and only if all elements of R that are not units form an ideal.   I understand that I need to prove both directions so:  $(\Rightarrow)$ Local ring means has a unique maximal ideal, so I want to show that this implies the elements are not units.  $(\Leftarrow)$ non unit elements of $R$ form an ideal, so if I show this is unique maximal ideal I can then conclude local ring?  Any hints would be appreciated. Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? Determining direction of longest segment of polygon using ArcGIS Desktop? I have a shapefile with 9000 agriculture fields and what I like to do is to determine for each field (=each polygon) the direction of the longest segment.  For instance, the selected polygon in the screenshot has its longest segment from west to east so I would like to mark give the polygon the attribute W (for west) or either E (for east).   Is there any solution to solve my problem in a fast but generalized way?   I do not need very detailed results. It's just for the interpretation of a question.   I'm seeking an answer using ArcGIS 10.2 for Desktop.  To be more precise on what I'm looking for I try to explain more practical: I'm doing winderosion analysis for a specific area with 9000 fields. As result I have a potential susceptibility for each field. I like to check, if the fields with high susceptibility are correlated to a certain orientation of the fields, e.g. check if most of the fields with high risk are oriented in the main winddirection or not.   The search for the longest segment is not really important for me. It was just an idea I had to determine the direction. So forget about the longest segment if there is a way to determine the direction with another method ;) Are the proofs for the properties of parallel lines, and that a triangle has 180 degrees, inherently tautological? I've noticed something while trying to prove the properties of parallel lines, and the properties that a triangle has 180 degrees. To prove the properties of parallel lines, such as alternate angles, you need to use the property that a triangle has 180 degrees. To prove a triangle has 180 degrees however, you need to use the properties of parallel lines. This really bothers me because of how circular it is. They are both reliant on each other to be true, and do not logically show, without being reliant on each other, why triangles have 180 degrees, and why parallel line properties are true.   So what I hoping for here is a way to prove parallel line properties without using the fact that a triangle has 180 degrees, or a way to prove triangles have 180 degrees without using parallel line properties. This way, things will be logical to me, and make sense.   Thanks in advance. What does it take to understand Maxwell's equations? Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in order to have the tools I need to make sense out of it?  I'm kindof looking for a road map which I can use to get started and know what to focus on. The fields are pretty big so some pruning would be very helpful (if possible) Shiny locked Legendaries in ORAS Serebii says that (probably) the only  in ORAS are Kyogre, Groudon, Rayquaza and Deoxys. This means that Reshiram and Zekrom, that were shiny locked in BW/B2W2, now can be found shiny.    Can anyone prove this? I'd like to know if it's true before waste hours in softresetting. Here is a sentence excerpted from ,     Teen suicide is a growing health concern. It is the third-leading cause of death for young people ages 15 to 24, surpassed only by homicide and accidents, according to the U.S. Center for Disease Control and Prevention.   I've heard people use both "people aged from X to Y" and "people ages from X to Y" quite often, but I've always been believing that only the former is grammatically correct, whereas in the latter the "ages" doesn't seem to serve as any grammatical component of this sentence. So when I see an APA paper use "ages" in that way, I am just quite surprised: I just can't believe such an authoritative and rigourous academic institution will let such an explicit (and indeed naive, even to a non-native speaker's eyes) grammatical mistake survive in their publications. I'm aware that in daily language usage one ought not to become so fussy over insignificant matters like this, but I do wonder whether it should be paid attention to in academic writings.  OR, using "ages" in that way is no longer considered a grammatical mistake? Honestly I don't think this'd be true, but if it really is, I'd be grateful to be informed. Thanks! I was surprised to find that standalone package can not compile a document with an equation:  \documentclass{standalone} \begin{document} \begin{equation} % not working! F(V, T) = E(V) + D(T) \end{equation} \end{document}   Is there an option or some workaround that allows this? The current error is something like:   ! Missing $ inserted.   in line 4. (The idea of course is that the including (main) document can just \input the standalone without knowing if is going to be an equation or something else) It is well known that compactness implies pseudocompactness; this follows from . I know that the converse does not hold, but what is a counterexample?  (A  is a topological space $S = \langle X,{\mathfrak I}\rangle$ such that every continuous function $f:S\to\Bbb R$ has bounded range.) How can I disable cloud-init? I have a fully-configured instance and an image from that for an autoscaling group. When autoscaling new instances from this image, it calls cloud-init. cloud-init changes the hostname and breaks fstab.  I want to prevent cloud-init from starting on instance launch. The company I work for has asked me to attend a training class on the other side of the country.  However my situation is my drivers license expired a few days ago. I do however have a separate printed email stating that the license has been renewed.  This drivers license is my only ID that shows both my name &amp; photo.  Is it possible to be able to board a flight with the expired drivers license and the printed email showing that it was renewed? Concurrent and Blocking Queue in Java When is $2^n -7$ a perfect square? This came up while solving another ENT problem. I want to ask when is: $$2^n -7 \text{ where } n\geq 3$$ a perfect square? Specifically, I also wanted to know what would be the solutions when $n$ is odd? How should I solve this?  I can check that $n=3, 4, 7$ are solutions but cannot find more. As it is of the form $4k+1$, it doesn't help as well. Are mounts proficient in armour (barding)? Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$ $$GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$$  This is trivial to prove with the first isomorphism theorem - by using the determinant as a endomorphism, then as $SL_n(\Bbb{R})$ is $1$ under the determinant, it is the kernel, and by FIT, the above is proved.  I was wondering how to prove this without the isomorphism theorem ? How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime Let us consider the ring $\mathbb{Z}_n$ where $\bar{m}\in\mathbb{Z}_n$  Could anyone help me prove that $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime  So far I have:  Assume $\exists \bar{a}: \bar{m} \bar{n}=n \mathbb{Z} \Rightarrow$ for some $b\in\mathbb{Z}:am=bn$  I then assumed $n,m$ were coprime and attempted to use $\exists a&#39;,b&#39;\in \mathbb{Z}:a&#39;m+b&#39;n=1$ to come to a contradiction, however haven't found one, the most promising thing I have found so far is that  $a=n(a&#39;b+ab&#39;)$ and $b=m(a&#39;b+ab&#39;)$ $\Rightarrow n|a$ and $m|b$ Why didn't the Order of the Phoenix assist with the trio (i.e.  Harry Potter, Ron Weasley and Hermione Granger) in the Horcrux hunt? What's the intuition behind "stiff systems"? How do I log every command executed by a user? I want to monitor all user's activity in my server.  Even when the user executes a shell command from some editor like vim I want to see them in the log file.  I have checked the tool acct but it is not listing the complete commands. (Please correct me if I have missed some options which does already).  Which Linux tool I should be looking at to solve this problem?