forecast(method ='arima') ; auto.arima() function, how to avoid forecast not in line with history?
ETS() function, how to avoid forecast not in line with historical data?
Second law of Newton for variable mass systems Frequently I see the expression  $$F = \frac{dp}{dt} = \frac{d}{dt}(mv) = \frac{dm}{dt}v + ma,$$ which can be applied to variable mass systems.  But I'm wondering if this derivation is correct, because the second law of Newton is formulated for point masses.   Furthermore if i change the inertial frame of reference, only $v$ on the right side of the formula $F = \frac{dm}{dt}v+ma$ will change, meaning that $F$ would be dependent of the frame of reference, which (according to me) can't be true.   I realize there exists a formula for varying mass systems, that looks quite familiar to this one, but isn't exactly the same, because the $v$ on the right side is there the relative velocity of mass expulsed/accreted. The derivation of that formula is also rather different from this one.   So my question is: is this formula, that I frequently encounter in syllabi and books, correct? Where lies my mistake. Is the Dungeon Magazine 4e Adventure List spreadsheet still available? used to go to a spreadsheet with all the 4E adventures published in Dungeon Magazine (and possibly some others, IIRC) during that edition's duration. I remember it listed out each adventure by name, start/end level, adventure path, and maybe even a little summary blurb.  However, the spreadsheet behind that link seems to have disappeared into the digital ether, and I can't find a copy of it in my own google drive (implying I never made a copy of it).  Does anyone happen to have a copy of that spreadsheet that they could share, and/or other resources that would let me sort through the many adventures from 4E Dungeon Magazine? "Naturally occurring" non-Hausdorff spaces? Using simple quotes "" instead of \text{} Is there a way to use newcommand or some other nice technique to transform any occurence of  "bla"   in math mode into  \text{bla}   The reason I ask is because it is easy, and doesn't interrupt the flow of reading the (La)TeX code as much.  I would like to keep Xe(La)TeX's nice quote behavior (ie it can use the regular "" instead of backticks to quote some text outside math mode). Evaluating: $\lim\limits_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$ I am trying to evaluate the following but without result.  $$\lim_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$$  Can you please give me some hints? I have tried to put log to both sides but it hasn't lead me somewhere... Thanks a lot #!/bin/bash - no such file or directory I've created a bash script but when I try to execute it, I get   #!/bin/bash no such file or directory   I need to run the command: bash script.sh for it to work.  How can I fix this? How can I take pictures through a skyscraper, airplane, or train window? How to change LCD brightness from command line (or via script)? To work around  (changing LCD brightness via hotkeys impossible), I'd like to have one command line query for increasing and one for reducing the brightness of my LCD. I could then map a hotkey to each one of this queries.  The problem is: I don't know how to increase and reduce the LCD brightness on the command line. Do you? Suppose that $S_0$ and A are positive numbers, let $$S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right)$$ with $n \geq 0 $.      (a)Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$       (b)Show that $S_{n+1} \leq S_n $ , if $n \geq 1$      (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists      (d) find s   (a) Show that $S_{n+1} \geq \sqrt{A} $ if $n \geq 0$  Given $$P_n:  S_{n+1} = \frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \geq \sqrt{A}$$  $$P_0: S_{1} = \frac{1}{2}\left(S_0 +\frac{A}{S_0}\right) \geq \sqrt{A}  $$  We assume that $P_n$ is true  $$P_{n+1}: S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right)$$ by assumption $$S_{n+2}= \frac{1}{2}\left(S_{n+1}\left(1 +\frac{A}{(S_{n+1})^2}\right)\right) \geq \frac{1}{2}\left(\sqrt{A}\left(1 +\frac{A}{(\sqrt{A})^2}\right)\right)$$ $$ S_{n+2}= \frac{1}{2}\left(S_{n+1} +\frac{A}{S_{n+1}}\right) \geq \sqrt{A}  $$  It follows that $S_{n+1} \geq \sqrt{A} $    (b) Show that $S_{n+1} \leq S_n $ , if $n \geq 1$  $$S_{n+1} \leq S_n$$ $$\frac{1}{2}\left(S_n +\frac{A}{S_n}\right) \leq S_n $$ Dividing by $S_n$ $$\frac{1}{2}\left(1 +\frac{A}{S_n^2}\right) \leq 1 $$ $$\frac{A}{2S_n^2} \leq \frac{1}{2}$$ $$A \leq S_n^2$$ $$S_n \geq \sqrt{A}$$ As  $S_{n+1} \leq S_n$ yields a true statement, it follows $S_{n+1} \leq S_n$ is true.    (c) Show that $s= \lim\limits_{n \rightarrow \infty} S_n$ exists  Since $S_{n+1} \leq S_n$, the sequence is non-increasing,   using the non-increasing theorem stating that      if $\{S_n\}$ is non-increasing then $$\lim\limits_{n \rightarrow &gt; \infty} S_n = \inf\{S_n\} $$     (d) find s    Is the argumentation in (a) and (b) appropriate? Also, I have to admit I m getting less confident in my argumentation (c) and (d). How to proceed in (c) and (d)?  Much appreciated for your input or help. Automatically Locate Included Images Do you think it's possible to include images into LaTeX without specifying the exact path to them. So instead of:  \includegraphics{path/to/image/myfig.pdf}   It would be:  \includegraphics{myfig.pdf}   While the image would still reside in the path/to/image/ directory. Basically, I'm asking if there is a macro that can recursively search for the image.  An alternative for me is to write a script outside of LaTeX that determines all the images that are included, performs the recursive search and copies those files temporarily in the same directory as the .tex file. Can't execute .out files, getting permission denied I have written a C++ program and complied it to produce a.out file. However, whenever I try to run it, I get Permission Denied. I read that we can use sudo, but I can't quite get it to work. I use something like, sudo "./a.out" but that too doesn't work.  Edit:  Here is the message I get when I try "./a.out".  bash: ./a.out: Permission denied I'm fairly new to blender and not a graphics person by any stretch of the imagination. I've been having some success though modelling semi-reflective glass for a project I wish to build (physically) and I'm wondering if it is possible to model the effects of a lens. The lens I wish to model is a double-convex type. It has a diameter of 120mm and a focal-length of 301mm. Is this something that can be modelled in blender and if so, how? I'd like to be able to position the camera close to this lens and reproduce the magnifying effects of the lens on the scene behind the lens as well as depth-of-field effects.  Thanks a lot. I created some texture maps in MindTex to use in Blender, but I can't figure out how to properly hook them up. The maps I have:  - Diffuse  - Normal  - Height   - Specular   - Gloss   - Self Illumination  - Reflection  - Ambient Occlusion   MindTex (left) vs. Blender (right)  As you can clearly see it's a pretty big difference.  is my material node setup in Blender. In the examples I don't actually use self illumination or reflection images, but including this in the answer would be helpful. Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem. This is different then the other versions of the questions here. I'm not supposed to use the diagonal argument. I'm looking to write a proof based on Cantor's theorem, and power sets. Error on Ubuntu boot up - "recovering journal" Trying to figure out what this means:    I got into the GRUB menu, chose Advanced Options, boot in recovery mode, login as root, and I did:  root@xps:~# sudo fsck -f / fsck from util-linux 2.27.1 e2fsck 1.42.13 (17-May-2015) /dev/nvme0n1p2 is mounted. e2fsck: Cannot continue, aborting.   Coincidentally, I am also seeing this fuzzy rainbow thing on the outside of desktop windows:    But now the machine won't even boot up at all. "Which" vs. "what" — what's the difference and when should you use one or the other? Most of the time one or the other feels better, but every so often, "which" vs. "what" trips me up.   So, what's the exact difference and when should you use one or the other? How to Create a Grid Inside a Polygon that is Oriented with the Longest Side? I have been using a process called "Create Polygon Graticule" to create a grid within a polygon with assigned row and column attributes. It is a SAGA tool which I have been running in QGIS. It generates a grid based on the extent of the input polygon with the cell running N to S and E to W. It would be better for my analysis if the direction of the grid was parallel to the longest edge of the polygon. For reference I have attached images of the current automated output and an output that I manually altered to align the grid with the polygon. The grids originally covered the entire extent of the polygon but have been clipped to show only the cell parts that are inside.    Above image is what the tool out puts by default.   This is an image of a grid that was edited manually to fit the necessary parameters.  My question is, is there a way to produce grids that are aligned such as the one in the second image in an automated fashion? I will need to generate grids for a few thousand polygons. Editing Gsettings unsuccesful when initiated from cron proof that every finite matrix has an annihilating polynomial asp.net mvc put controllers into a separate project I'm just learning asp.net mvc and I'm trying to figure out how to move my controllers into a separate project.  Typically when I have designed asp.net web apps before, I created one project for my models, another for my logic, and then there was the web.    Now that I'm learning asp.net mvc I was hoping to follow a similar pattern and put the models and controllers each into their own separate projects, and just leave the views/scripts/css in the web.  The models part was easy, but what I don't understand is how to make my controllers in a separate project be "found".  Also, I would like to know if this is advisable.  Thanks!