In ArcMap, when I zoom out (or in) a single mouse-click (not dragging a rectangle, just a click), what is the change to the ratio?  If it is different between coordinate systems please explain it on GCS_WGS_1984.
I only occasionally use the Fixed Zoom In/Out buttons on the Tools toolbar of ArcMap and had always assumed that they zoomed in/out by a set scale factor.  However, using ArcGIS for Desktop 10.2, I just set my scale to be 1:10,000,000 and then hit the Fixed Zoom In button 10 times while recording the subsequent scale each time and was surprised to see:  10,000,000 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,500,000 2,000,000 1,500,000 1,250,000 1,000,000   Dividing each scale denominator by its successor shows a sequence of: 1.25, 1.33, 1.2, 1.25, 1.33, 1.2, 1.25, 1.33, 1.2  Curious about what happened in between the scales above I experimented a little to discover that the first issuance of the Fixed Zoom In button simply takes the scale to the first of those listed above and then starts following the same pattern.  Try starting with 1:8,000,001 to see ...  8,000,001 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000   This seems like quite a neat solution, but not one that I had realised was in place - does anyone know if it has been documented anywhere?    I've looked in the Online Help without success.  In answer to @DevdataTengshe, the scales currently in my available list (see below) seem to bear no relation to those used by Fixed Zoom In/Out.    However, when I add 1:7,500,000 into my available list it does seem to insert that as an additional scale step ...  10,000,000 8,000,000 7,500,000 6,000,000 5,000,000 4,000,000   This makes the algorithm being used even more mysterious to me.
Triangle Inequality for norm integral $\|f\|_1=(\int_a^b [|f|^2+|f'|^2]\mathsf dx)^{1/2}$. Define $C_1^1[a,b]$ to be the space of continuously differentiable functions on $[a,b]$, with norm $$\|f\|_1=\left(\int_a^b[|f|^2+|f'|^2]\mathsf dx\right)^{1/2}.$$ Show that this is a proper definition of a norm. Is this normed space complete?  I'm stuck on the triangle inequality part. I'm having a hard time showing that $$\|f+g\|_1\leq \|f\|_1+\|g\|_1.$$ Any hints or solutions are greatly appreciated. What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? Jquery, changing background image with timer Inverting direction of mouse scroll wheel Is there a way to make a mouse scroll wheel invert its direction? I'd like to scroll upwards and have that action scroll downwards and vice-versa. There is no setting on the Mouse control panel that makes this possible.   Any pointers to a hack or a particular mouse model that has such a setting would be appreciated. I am using Windows 7. Rich Snippets not working (and working at the same time?) Q1. Find the general solution to the difference equation  $$ a_{n} - 4a_{n-1} + 3a_{n-2} = 6 $$    Q2. Solve the difference equation   $$ a_{n} - a_{n-1} - 2a_{n-2} = 0, a_0 = 2, a_1 = 4 $$    I am completely lost in solving recurrence relation questions. Can anyone guide me in steps to solve the following 2 questions? How to undelete a directory that was just deleted with "rm -R" command (in cloud drive)? I deleted an important directory with rm -R command. This is an very populer host data. It was located /var/zpanel/hostdata/ayrintilih After remove ayrintilih directory has gone everything.  I tried to undelete with ext4magic program. But it need to another hdd volume for recovery.  Error message:   ERROR: can not use "/root/recoveried" for recover directory. It's the same filesystem : "/dev/dm-0"   My ISP just replied my request:  Unfortunately there is no way to add another Volume to a virtual Instance.  If it would be a dedicated Server, we could do it, but not in a Cloudserver.  You could try to minimize the partition and create another one, that would  count as another Volume. We also recommend to have allways a  Backup for your Important files. Etymological origin of "deosil" and "widdershins" How to intuitively understand eigenvalue and eigenvector? I'm learning multivariate analysis and I have learnt linear algebra for two semester when I was a freshman.  Eigenvalue and eigenvector is easy to calculate and the concept is not difficult to understand.I found that there are many application of eigenvalue and eigenvector in multivariate analysis. For example     In principal components, proportion of total population variance due   to kth principal component equal    $$\frac{\lambda_k}{\lambda_1+\lambda_2+...\lambda_k}$$   I think eigenvalue product corresponding eigenvector has same effect as the matrix product eigenvector geometrically.   I think my former understanding may be too naive so that I cannot find the link between eigenvalue and its application in principal components and others.   I know how to induce almost every step form the assumption to the result mathematically. I'd like to know how to intuitively or geometrically understand eigenvalue and eigenvector in the context of multivariate analysis(in linear algebra is also good).  Thank you! Linux "top" command: What are us, sy, ni, id, wa, hi, si and st (for CPU usage)? When I issue top in Linux, I get a result similar to this:    One of the lines has CPU usage information represented like this:  Cpu(s): 87.3%us,  1.2%sy,  0.0%ni, 27.6%id,  0.0%wa,  0.0%hi,  0.0%si,  0.0%st   While I know the definitions of each of them (far below), I don't understand what these tasks exactly mean.   hi - what does servicing hardware interrupts mean? si - what does servicing software interrupts mean? st - they say it's the "CPU time in involuntary wait by the virtual CPU while hypervisor is servicing another processor (or) % CPU time stolen from a virtual machine".   But what does it actually mean? Can someone be more clear?  I listed all of us, sy, ni, etc, because it could help others searching for the same. This information is not in the man pages.  us: user cpu time (or) % CPU time spent in user space sy: system cpu time (or) % CPU time spent in kernel space ni: user nice cpu time (or) % CPU time spent on low priority processes id: idle cpu time (or) % CPU time spent idle wa: io wait cpu time (or) % CPU time spent in wait (on disk) hi: hardware irq (or) % CPU time spent servicing/handling hardware interrupts si: software irq (or) % CPU time spent servicing/handling software interrupts st: steal time - - % CPU time in involuntary wait by virtual cpu while hypervisor is servicing another processor (or) % CPU time stolen from a virtual machine I have a laptop which I hook up to an external display when I'm at home. I also connected an external keyboard and mouse which makes it more comfortable for me.  I have noticed that pressing caps lock on the external keyboard does not light up the capslock indicator of the laptop keyboard (and vice versa).  When googling, I came across the setleds function, but when I type it into a console all I get is this:  KDGKBLED: Inappropriate ioctl for device Error reading current flags setting. Maybe you are not on the console?   Any idea if I can get this working? A subring of the field of fractions of a PID is a PID as well. Let $A$ be a PID and $R$ a ring such that $A\subset R \subset \operatorname{Frac}(A)$, where $\operatorname{Frac}(A)$ denotes the field of fractions of $A$. How to show $R$ is also a PID?   Any hints? When and how did "pretty" enter English as an intensifying adverb? Scattering, Perturbation and asymptotic states in LSZ reduction formula I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix element $\langle f|S|i\rangle$ as the eigenstates of the full Hamiltonian i.e., $H=H_0+H_{int}$. Therefore, the states $|i\rangle=|k_1 k_2\rangle$ is defined as $$|k_1 k_2\rangle=a_{k_1}^{\dagger}(-\infty) a_{k_2}^{\dagger}(-\infty)|\Omega\rangle$$ where $|\Omega\rangle$ is the vacuum of the full interacting theory. Then the LSZ reduction formula connects the S-matrix element $\langle f|S|i\rangle$ to the Green' functions of the interaction theory defined as $$G^{(n)}(x_1,x_2,...x_n)=\langle \Omega|T[\phi(x_1)\phi(x_2)...\phi(x_n)]|\Omega\rangle.$$ Here are a few doubts. Doubt 1 When the particles are far away, the interaction can be considered to be adiabatically switched off. Therefore, at $t=\pm\infty$ the states are really free particle states and should have been written as $$|k_1 k_2\rangle=a_{k_1}^{\dagger}(-\infty) a_{k_2}^{\dagger}(-\infty)|0\rangle$$ and $$|k_3 k_4\rangle=a_{k_3}^{\dagger}(+\infty) a_{k_4}^{\dagger}(+\infty)|0\rangle$$ where $|0\rangle$ is the vacuum of the free theory.  I do not understand why these the states $|i\rangle$ and $|f\rangle$ are derived from $|\Omega\rangle$ instead of $|0\rangle$. Doubt 2 The initial and final states were derived from the vacuum of the interacting theory $|\Omega\rangle$. According to my understanding, this suggests that the states $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$  are eigenstates of the full Hamiltonian $H$. Since then there is no perturbation, there should not be any scattering or transition at all.  More references Even Peskin &amp; Schroeder, Bjorken &amp; Drell, Srednicki take the same approach as Schwartz; they too define the external momentum eigenstates to the eigenstate of the full Hamiltonian $H$. However, if the system was initially in a stationary state why should it undergo a transition in absence of any perturbation? How can I rename many files at once? I need to rename a bunch of files in order to fix their sort order, therefore I need to be able to do a sort of "find and replace" so I can replace chunks of the filenames at a time.  What tools should I use? I prefer GUI but a command line tool recommendation would also be fine. LED light fixture glows when not turned on This past week at Menards I bought 2 Smart Electrician® 3650 Lumens 46" LED Linkable Shop Light Model Number: 0053-0011  |  Menards® SKU: 3481400.  The LED shop light fixture has a glow to it. Looked like the LEDs were turned on, but not all the way. The power switch is turned off. Don’t know why I did this but I took one of those three prong adaptors converters to two prong and to my surprise the light fixture didn’t light up. I unplug the cord with the adaptor and turned it around and it still didn’t light up. The power supply electronics inside the light fixture must be using the earth ground wire somehow. Using my volt meter. I measured to earth ground to the green wire that comes out of the adaptor and to my surprise depending how I plug in the adaptor. I’m getting 112 volts AC. That's because the adaptor isn't keyed and I'm switching the HOT and NEUTRAL around depending how I  plug it in.  I connected the LED light fixture to “Safety Analyzer tester”. When I press the “Open Ground” button, the fixture stops glowing (lightly lite LED’s).  Looks like the power supply circuit inside the fixture has a connection to “Earth Ground”.  I then switched the “Normal” on the polarity switch to “Reverse” and the LED’s were off. Switching the Neutral to open position has no effect. I'm thinking of taking them apart and see inside what's going on or take them back.  I figured out the problem.    In this light fixture you can clearly see the white wire (neutral/common) is connected to the light switch, turning the power off the LED light strip. Commonly we switch off the “HOT” to your light socket so when you change your bulb you have a less of a chance of getting electrocuted (that’s another story for later). Sometimes in Power supply circuits they place capacitors in there to help filter electrical noise out. Also known as suppressers (electronics to reduce unwanted noise or oscillation in a circuit or unwanted frequencies in a signal). Depending on how or where they are placed in the circuit it could possible cause some issue if not installed correctly or if the circuit isn’t designed correctly.   Since the BLACK live wire is connected to the LED PCB all the time, anything connected to that line will potentially be LIVE voltage, that way when I disconnected the earth ground from the socket and measured 112 volts on it. My guess is they have capacitors connected to both LIVE and NEUTRAL to the earth ground wire.  The current is flowing through capacitor C2, just enough to turn the LED’s on slightly. If the switch was on the hot side, this problem wouldn’t be happening. I still may use them just not connect the “earth ground” wire. Because that’s providing the return path for lighting the LED’s. In Ubuntu 18.04 I'm not able to assign Ctrl+Alt+← or Ctrl+Alt+→ to anything. To be precise I may bind it to something, but it doesn't work when using the keyboard combination, up/down arrows do however work.   .  The strange thing is that the system detects the keyboard combinations when assigning a key, but not when trying to use them. As a result the keyboard combinations don't work in any other programs either. Difference in meaning and use of future perfect forms Why are potential differences equal across two capacitors in parallel, but charge on each capacitor is not? Two or more capacitors are said to be connected in parallel if each one of them is connected across the same two points. In a parallel combination of capacitors potential difference across each capacitor is same but each capacitor will store different charge. Why is this true? Why is the potential difference across each capacitor in parallel the same and why will each capacitor store different charge?  Also, in series, why are Potential difference across each capacitor different, while charge is the same? I'm looking for a way of saying “having amorous affairs”. Ideally it should indicate a married man fooling around with younger women, and the expression should be informal, humorous, in low register but yet not rude.