I want to use four pins on an Arduino Uno as digital inputs pins for four 12V DC outputs. I know I have to use a voltage divider first (with resistor values being 14kOhm and 10kOhm) to get the correct voltage range (0-5V) and also use the internal 20kOhm resistors on the Uno to achieve this.   My first idea was to not use the internal resistors on the Uno, but instead use external ones, to pull the voltage to zero, when nothing is connected to the input (prevent floating values). A colleague suggested the usage of the internal pullups on the Arduino, but I have no idea how to wire this up now.  Can someone explain it to me somehow?
I am creating a controller for a 12 V system using an Arduino Uno microcrontroller. For the outputs I am using a relay shield to switch the 12 V components. I have a 12 V toggle switch that turns on some 12 V components in the system and I want to use a trigger signal off of this same switch to send to an Arduino digital input. I know that the Arduino can only handle 5 V max. What would be the best way to step down the 12 V coming off of the switch to the 5 V for the input?  EDIT: The system is for use in a car. Would the amperage of the car battery need to be lowered somehow as to not blow up the components?
Prove holomorphism of expression I have to prove that given $\gamma$ contour of $G \subset \mathbb{C}$  and $f$ continuous function on $G$. Then the function $g(z) = \int_{\gamma} \frac{f(w)}{w-z}dw$ is holomorphic on $\mathbb{C} - \bar{G}$ My attempt: I started by using that given any parametrization $\alpha :[a,b] \rightarrow \gamma$ we can rewrite $g(z)$ as: $g(z) = \int_a^b \frac{f(\alpha(t))}{\alpha(t)-z}\alpha'(t)dt$ Now using the fundamental theorem I derivate to see where $g'(z)$ is defined and I get: $g'(z) = \frac{f(\alpha(b))}{\alpha(b)-z}\alpha'(b) - \frac{f(\alpha(a))}{\alpha(a)-z}\alpha'(a) $ Here I get stuck, I fail so see how this links back to $g$ being holomorphic at $\mathbb{C} - \bar{G}$. Any hints on how to proceed? Thanks! Use of *args and **kwargs I had always kind of wondered why we didn't see interference in things like windows -- we were taught that the condition is that the thickness of the film/slab/medium just has to be an integral number of wavelengths, $d=m\lambda$. My logic was, if visible light has wavelengths ~400-780nm, any window pane has got to be an integral number of wavelengths (or close to integral) for some of the wavelengths in the visible.  For example, if a window is, $6mm = 6\times10^6nm$ thick, then you should see interference for wavelengths (and some range around them) 200nm, 250nm, 300nm, 400nm, 500nm, 600nm... Because 6mm is an integral number of each of those.  Obviously that would be really annoying and isn't the case. I found  (warning: PDF) source that seems to explain it and I was wondering if what they're saying is sound. On the 10th page (p171 for them), it says that the reason we don't see this interference is that no window is that smooth, it has a variance in the thickness of at least several wavelengths, so the interference effect is effectively average out among all those thicknesses, which usually gets rid of it. They do the math and show that.  Is that the reason?  If so, that leads me to two questions: Could we, if we were really careful and used something like MBE, make a glass window with that sort of accuracy, and then see interference effects in the optical range? I know that quartz crystal monitors can easily give you nanometer accuracy for evaporators and sputterers, but they also have pretty limited growth rates.  My second question is, then, do we see interference effects in glass windows with electromagnetic radiation of a comparable wavelength, like microwaves?  Thanks! Using the variable "name" doesn't work with a JS object Recently I've installed Kubuntu in a newly bought laptop with an Intel WiFi 6 AX200 network card, I can connect to the wifi without apparent problems but when I open the driver manager in the settings I face this weird situation:  Intel Corporation: Wi-Fi 6 AX200 This device is not working.  [ ] Using iwlwifi driver backport in DKMS format from backport-iwlwifi-dkms (open source)  [ ] Continue using a manually installed driver  [x] Do not use the device   Note that "Continue using a manually installed driver" is the only voice selectable in the list.  Here is some additional information:  $ lspci -nnk | grep 0280 -A3 02:00.0 Network controller [0280]: Intel Corporation Wi-Fi 6 AX200 [8086:2723] (rev 1a)         Subsystem: Intel Corporation Wi-Fi 6 AX200 [8086:0084]         Kernel driver in use: iwlwifi         Kernel modules: iwlwifi  $ rfkill list all 0: hci0: Bluetooth         Soft blocked: yes         Hard blocked: no 1: phy0: Wireless LAN         Soft blocked: no         Hard blocked: no  $ dmesg | grep iwl [    2.888227] iwlwifi 0000:02:00.0: enabling device (0000 -&gt; 0002) [    2.945179] iwlwifi 0000:02:00.0: Direct firmware load for iwlwifi-cc-a0-50.ucode failed with error -2 [    2.945217] iwlwifi 0000:02:00.0: Direct firmware load for iwlwifi-cc-a0-49.ucode failed with error -2 [    2.947244] iwlwifi 0000:02:00.0: TLV_FW_FSEQ_VERSION: FSEQ Version: 43.2.23.17 [    2.947250] iwlwifi 0000:02:00.0: Found debug destination: EXTERNAL_DRAM [    2.947252] iwlwifi 0000:02:00.0: Found debug configuration: 0 [    2.947697] iwlwifi 0000:02:00.0: loaded firmware version 48.4fa0041f.0 op_mode iwlmvm [    3.145585] iwlwifi 0000:02:00.0: Detected Intel(R) Wi-Fi 6 AX200 160MHz, REV=0x340 [    3.159226] iwlwifi 0000:02:00.0: Applying debug destination EXTERNAL_DRAM [    3.160060] iwlwifi 0000:02:00.0: Allocated 0x00400000 bytes for firmware monitor. [    3.336456] iwlwifi 0000:02:00.0: base HW address: 50:eb:71:d7:0b:40 [    3.353553] iwlwifi 0000:02:00.0 wlp2s0: renamed from wlan0 [    4.457920] iwlwifi 0000:02:00.0: Applying debug destination EXTERNAL_DRAM [    4.621843] iwlwifi 0000:02:00.0: FW already configured (0) - re-configuring [    4.629999] iwlwifi 0000:02:00.0: BIOS contains WGDS but no WRDS   Someone have idea why this happened? I'm building an object detector using HOG features and linear SVM. Some of the regions of the object are more "distinctive" so I would like to give more weight to the features extracted from those regions. (e.g. imagine we want to detect between mugs and glasses, then the most "distinctive" part is the mug's handle)  How could I do this? For sure there should be a more intelligent way than just replicating the features of those "distinctive" regions. Search All Fields In All Tables For A Specific Value (Oracle) If development on the Stack Exchange iOS/Android apps has ceased indefinitely, what should we do to their bug reports and feature requests? It's been a while since the Stack&nbsp;Exchange team last had an iOS or Android developer, and the development job on the apps have not had any insights for years.  That, however, doesn't deny the fact that there are still many users to them. As a consequence, people are continuing to submit bug reports and sometimes feature requests about them.  If development on iOS/Android apps has ceased indefinitely, what should we do to their bug reports and feature requests?  Are we going to keep them with the hope that development on apps will resurrect one day, or just ignore them and telling users that development has frozen? When to use an object pronoun or a possessive adjective before a gerund Question Regarding Cardano's Formula In Cardano's derivation of a root of the cubic polynomial $f(X)=X^3+bX+c$ he splits the variable $X$ into two variables $u$ and $v$ together with the relationship that $u+v=X$. From this he finds that $x=u+v$, where  $$u=\sqrt[3]{\frac{-c}{2}+\sqrt{\frac{c^2}{4}+\frac{b^3}{27}}}$$ and $$v=\sqrt[3]{\frac{-c}{2}-\sqrt{\frac{c^2}{4}+\frac{b^3}{27}}}$$  is a root of $f(X)$.      Is there an intuitive explanation for why Cardano splits the variable $X$ into two parts, $u$ and $v$? wrong numbering for subcaption in scrbook When using the scrbook document class in combination with the subcaption  package, the numbering of subfigures seems broken. Consider:  \documentclass{scrbook} \usepackage{xcolor} \usepackage{caption} \usepackage{subcaption} \captionsetup{%   format=hang,%   font=small,%   labelfont={sf,bf},%   aboveskip=0.2\normalbaselineskip,%   position=top } \pagestyle{empty}  \begin{document} \begin{figure}   \caption{Black}   \label{fig1}   \centering \rule{2cm}{2cm} \end{figure}  \begin{figure}   \caption{More figures}   \label{fig2}   \centering   \begin{subfigure}{.3\textwidth}     \centering     \caption{Blue}     \label{fig2a}     \color{red}\rule{2cm}{2cm}   \end{subfigure}   \begin{subfigure}{.3\textwidth}     \centering     \caption{Green}     \label{fig2b}     \color{green}\rule{2cm}{2cm}   \end{subfigure}   \begin{subfigure}{.3\textwidth}     \centering     \caption{Blue}     \label{fig2c}     \color{blue}\rule{2cm}{2cm}   \end{subfigure} \end{figure}  Figure \ref{fig1} shows a black box. Figure \ref{fig2} shows colored boxes, where Figure \ref{fig2a} shows a red box, Figure \ref{fig2b} shows a green box, and Figure \ref{fig2c} shows a blue box. \end{document}   This results in the following display:    Clearly, the figure numbering in the text references is off by one for the subfigures. Instead, if I change the document class to article, it looks fine:     Why does this happen, and how can I prevent it? I am wondering what sudo apt-get update does?  What does it update? What is wrong with defining \bal as \begin{align}? I'm trying to define two commands \bal and \eal instead of inserting \begin{align} and \end{align} in my document, but in the code below, I'll get some errors. What is wrong with it?    \documentclass{article} \usepackage{amsmath} \makeatletter  \newcommand{\bal}{%  \begingroup  \align% \@ifstar{\nonumber}{}%  }  \newcommand{\eal}{\endalign\endgroup} \makeatother \begin{document} \bal* x=y \eal ‎\end{document} What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors? I get the physical significance of vector addition &amp; subtraction. But I don't understand what do dot &amp; cross products mean?   More specifically,    Why is it that dot product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\cos\theta$? Why is it that cross product of vectors $\vec{A}$ and $\vec{B}$ is defined as $AB\sin\theta$, times a unit vector determined from the right-hand rule?   To me, both these formulae seem to be arbitrarily defined (although, I know that it definitely wouldn't be the case).   If the cross product could be defined arbitrarily, why can't we define division of vectors? What's wrong with that? Why can't vectors be divided? Measuring accuracy of latitude and longitude? Can the ship's captain really perform your wedding when in international waters? On , Mark Mayo posted a comment that any marriage has to be on dry land or close to it.  But I'm sure all of us have heard of ships' captains marrying couples at sea.  From the movie Casablanca:     Say, why don't we get married in Marseilles?   ...   Well, let's see. What about the engineer? Why can't he marry us on the train?   ...   Well, why not? The captain on a ship can. It doesn't seem fair that...    So is this fiction after all? If not how does it fit with Mark's comment? What special rules and such should we know?  If I'm travelling at sea with a significant other and wish to tie the knot, can we do so with any captain on any ship on any sea? Must it be international waters? How to run a scheduled job every 15 minutes? Using the salesforce GUI it seams impossible to schedule a job every 15 minutes. Or more than once a day. Tiny navigation buttons and tags on responsive mobile I know it will be hard for you to tell on desktop because the resolution is so high, but the clickable text in the upper left, the icons on the upper right, and the navigation buttons at the bottom are all tiny. I have to squint to read the tags, I can't reasonably tap any navigation button except for Next without zooming, and selecting the achievements dialog, etc. is all very difficult. It seems to me that this would not be terribly difficult to change, so I am posting this feature request. I'm using a relatively large Samsung phone (Note 8), so I can imagine it would be worse on smaller phones.  Edit: I see from posted images that the responsive design on other phones looks nothing like mine. I'm wondering if it has something to do with the high resolution  where it thinks it is bigger than it is, or it's picking the wrong sizes because it's a tiny bit over some size threshold, in which case this would be a bug. I just signed up, a day or two ago, and I've received a notification that there's something in my inbox.  Unfortunately, my email client isn't able to show me a link to my Inbox, or the message, because of the format of the email.  I normally use the email address that I gave when I signed up, just with MailWasher, which is intended to safely preview emails, as plain text, to decide whether or not to open them in a normal HTML email client.  I would be nice if that email contained a link to my inbox, which could be shown in MailWasher.  In order to collect that email in a normal email client, I'd also have to collect or delete all the other emails sent to that address.  I'm not entirely clear what's been done in that email to stop MailWasher seeing the link.  I can see a link to leave feedback, and one to unsubscribe, but not one to check my inbox.  Sure, I can live without one, but those emails would be a lot more useful to me if I could just click a link to go to my Inbox. Periodically, my MacBook Pro 17" stops recognizing my headphones. No amount of unplugging and replugging seems to help. The sound settings never show headphones as an output device. How can I fix this? The only thing I can find elsewhere on the Internet are people saying, "Reboot!" This works, but is impractical and annoying.