I'm trying to mount this light on the exterior of a house, but it doesn't cover the hole like the existing lights do.  In some places there's an existing light that's mounted directly to a junction box, and in others, I'm installing a light for the first time.  How should a light like this be mounted in a way that's up to code and prevents water from entering the house?
I'm considering replacing an outdoor lighting fixture with an LED motion-sensitive fixture, but I'm not sure how to safely do the wiring.  The location is protected (under a porch) but still needs to be weatherproof. Here's the existing fixture and mount:    The obvious replacement would be another lamp that included its own box cover, so that its wiring would be covered and protected. But, the fixture I like doesn't include such a cover:    You can see it's meant to be screwed into the wall, but doesn't cover anything. The power cable ends with bare wires which are meant to be wire-nutted to the supply wiring, probably inside a junction box. But, how do I get the wire safely into the junction box while keeping things weatherproof?  One option would be to replace the lamp's power cable with one ending in a grounded plug, and install a weatherproof outlet box. But that's ugly and complex.  Are there weatherproof junction box covers that include provisions for sealed entry of cables?
I recently tried to change a bulb using an adaptor (converting from a E27 to B22 fitting). After switching on the light fitting the fuse had blown. After inspection it turns out the adapter is faulty and must have caused a short-circuit.  After removing the bulb and resetting the switch in the main fuse box, I am now unable to operate the switch on the wall to turn the fitting off (the switch physically won't click).   Is there something I can do to fix the problem?  Thanks, I have been reading about depth-of-field and presume to have a sufficient understanding of what it means and how it is related to lens properties, lens aperture, focal length, sensor format size and probably even print dimensions in case the picture is being printed. I do have a question about how/if depth-of-field depends on the dimension of a pixel. Let me elaborate:  Given two sensors with differing pixel sizes: x and 4x, the latter sensor integrates more light per-pixel than the former, however, it might have a lower resolution if the sensor dimensions remain fixed. Theory suggests that the depth of field is determined by those circles-of-confusion which are very close to being an in-focus point, and this perhaps also means that these very small CoCs fall within the integration area of the same pixel. Now when a CoC becomes larger than a pixel (like also in the case of diffraction blur), there is some spreading of intensities among neighboring pixels and this would clearly lead to blur. However, if one was using the 4X sized pixel, even with a slightly larger CoC, the intensity would still integrate into the same pixel area, and would thus perhaps be in-focus? Is this the right assumption? And if so, is there any analysis of pixel-area dependence of depth-of-field? Moreover, depth-of-field is in some sense independent of the integration medium as it clearly occurs in analog film devices as well, so is there a trade-off or a difference in depth-of-field between film and digital cameras?  Please point me to the correct references for this question. Please correct me if there seems to be a fundamental issue with the assumptions made above. Apply brace expansion in "reverse order" Error Message:      "A reboot is pending. Please restart before starting Visual Studio".    I installed Visual Studio (Visual Basic 2015 and SQL 2015) and after what looked like a successful install I then got the "Reboot" window.   Not expecting it I had a bunch of things open. So I closed a bunch a bunch of things, and did the reboot myself.   Now I cannot run Visual Basic because it ONLY gives me the above error message in the pop-up window. It won't even let me do a re-install.   All it does is keep giving me the above error message.   If you have any advice that's better than a complete uninstall/reinstall I'm sure everyone in my situation would benefit from it.  How can I resolve this issue? How can I list the contents of a .zip folder in c#? Which Distribution Does the Data Point Belong to? The editor asked me to use the following format.      Reference   1. Author, blah blah   Instead of      Reference   [1] Author, blah blah ...   Even though in the main text, [1] style has been used.   For example,        Smith [1] has proposed ...      Reference   1. Smith,      This is what I want.   Could you please advise how I can do the above?  Thanks in advance. Workarounds for Sites page to update standard object? SQL Server nvarchar(max) vs nvarchar(n) affects performance How to prove Fibonacci sequence with matrices? What is the definition of "creature" and is it used consistently? Find a recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s or two consecutive 1s. How to use unicode characters in Windows command line? We have a project in Team Foundation Server (TFS) that has a non-English character (š) in it. When trying to script a few build-related things we've stumbled upon a problem - we can't pass the š letter to the command-line tools. The command prompt or what not else messes it up, and the tf.exe utility can't find the specified project.  I've tried different formats for the .bat file (ANSI, UTF-8 with and without ) as well as scripting it in JavaScript (which is Unicode inherently) - but no luck. How do I execute a program and pass it a Unicode command line? The  says that there is a moderator election occurring.   How does the election work and how can I get involved? $P(\limsup A_n)=1 $ if $\forall A \in \mathfrak{F}$ s.t. $\sum_{n=1}^{\infty} P(A \cap A_n) = \infty$ Let $\mathfrak{F} = (A_n)_{n \in \mathbb{N}}$. Prove that $P(\limsup A_n)=1$ if $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$. (Side question 1 Is second Borel-Cantelli out because we don't know if the $A_n$'s are independent?)  Suppose $\forall A \in \mathfrak{F}$ s.t. $P(A) &gt; 0, \sum_{n=1}^{\infty} P(A \cap A_n) = \infty$, but $P(\limsup A_n)&lt;1$. My prof gave us this convenient hint: Show $\exists M &gt; 0$ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$.  $1 &gt; P(\limsup A_n)$  $1 - P(\limsup A_n) &gt; 0$  $P(\liminf A_n^{c}) &gt; 0$  By definition of $\liminf A_n^{c}$, $\exists M &gt; 0 $ s.t. $P(\bigcap_{j=M}^{\infty} A_j^{c}) &gt; 0$. (Side questions 2 and 3 Isn't this =1? ...Wait, is that what we're trying to prove? Haha)  $\to 1 - P(\bigcup_{j=M}^{\infty} A_j) &gt; 0$  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j)$  Main question: Now I guess we have to come up with some A s.t.  $\to 1 &gt; P(\bigcup_{j=M}^{\infty} A_j) \geq \sum_{n=1}^{\infty} P(A \cap A_n)$, or is there something else to do? Flash with Chromium or Google Chrome broken on Ubuntu 19.04 I tried loading Adobe Flash player in Chromium on Ubuntu 19.04 (Lubuntu in this case) using various answers on AskUbuntu.com. I get to the point where the Allow Flash popup happens. But when I click to allow it, it says "Right-click to run Adobe Flash Player". When I rightclick and choose Run this Plugin, nothing happens. I've tried to apply fixes using the Pepperflash technique, as well as the Adobe Flashplugin technique. $ versus jQuery Nested roots sequence, how to prove it's monotone and bounded? Let $a\ge1$ and define the sequence $(x_n)$ recursively by: $$x_1 = \sqrt{a}$$ $$x_{n+1}= \sqrt{a+x_n}$$  Here's what I did:  Plugging in some values makes it seem as if the sequence is increasing. I first solve the equation $t=\sqrt{a+t}$, equivalently $t^2 -t -a =0$, to get an idea what's going on. The roots are $$t_{1,2}= \frac{1 \pm \sqrt{1+4a} }{2}.$$ Therefore, between the roots, that is for $$t\in \left( \frac{1 - \sqrt{1+4a} }{2}, \frac{1 + \sqrt{1+4a} }{2}\right)$$  we have $t^2-t-a \le 0 \iff t \le \sqrt{a+t}$. Here's my attempt at showing inductively that $$\forall n\in \mathbb{N}, \ x_n \le \frac{1 + \sqrt{1+4a} }{2}$$  For $n=1$, the statement is true (simple arithmetic). Suppose it's true for $n$. Consider  $$x_{n+1}= \sqrt{a+x_n}\le \sqrt{a+\frac{1 + \sqrt{1+4a} }{2}}=\frac{1 + \sqrt{1+4a} }{2},$$  because $\frac{1 + \sqrt{1+4a} }{2}$ satisfies $x=\sqrt{x+a}$.  So this establishes the sequence $(x_n)$ is bounded. Now, by induction again, I try to show it's monotonically increasing. The base case $x_1\le x_2$ is obvious. Assume (strong induction) $x_{n-1}\le x_n$ for all $n&gt;1$. But since we have $$x_1\le x_n \le \frac{1 + \sqrt{1+4a} }{2}, $$   then $x_n$ lies in the appropriate interval, so $x_n \le \sqrt{a+x_n}=x_{n+1}.$  Is this proof correct? Can the condition on $a$ be relaxed to $a&gt;0$? Maybe even small negative $a$? And could someone provide me with another proof of convergence of $x_n$? I absolutely hate this one! Can someone please give me some intuition as to when to choose either SVM or LR? I want to understand the intuition behind what is the difference between the optimization criteria of learning the hyperplane of the two, where the respective aims are as follows:     SVM: Try to maximize the margin between the closest support vectors LR: Maximize the posterior class probability    Let's consider the linear feature space for both SVM and LR.  Some differences I know of already:   SVM is deterministic (but we can use Platts model for probability score) while LR is probabilistic. For the kernel space, SVM is faster (stores just support vectors) How did Draco apparate within Hogwarts?