parallel configuration of diode I want to connect diodes in parallel to increase the current carrying capacity. If I connect two diodes in parallel having same rating(same forward voltage drop), does thermal runaway still come in picture? If forward voltage drop is not going to be same for each diode then why so when I'm using same diode?
Is paralleling diodes a bad idea? I'm trying to repair an 800W power supply (see my previous question on this.) One thing that gets me is that the design has two schottky diode packages (in TO-220) in parallel. I was always told this was A Bad Idea, but since they are thermally coupled to the same heatsink, does it present a problem in this instance? I've also noticed the same for the input bridge rectifier, two are used in parallel.
Boy and girl paradox is driving me crazy In the simple harmonic oscillator model, we talk about the angular frequency and I understand that this tells something about the instantaneous angular velocity of the object. For example, a simple pendulum. But what does this mean when we apply this concept to an object attached to a spring that behaves as a simple harmonic oscillator? There is no instantaneous circular motion for the object, so how can we relate the angular frequency to a system like this? Check if specific id element exist Gradient descent and many other methods are useful for finding local minima in cost functions. They can be efficient when the cost function can be evaluated quickly at each point, whether numerically or analytically.    I have what appears to me to be an unusual situation. Each evaluation of my cost function is expensive. I am attempting to find a set of parameters that minimize a 3D surface against ground truth surfaces. Whenever I change a parameter, I need to run the algorithm against the entire sample cohort to measure its effect.  In order to calculate a gradient, I need to change all 15 parameters independently, meaning I have to regenerate all the surfaces and compare against the sample cohort way too many times per gradient, and definitely way too many times over the course of optimization.  I have developed a method to circumvent this problem and am currently evaluating it, but I am surprised that I have not found much in the literature regarding expensive cost function evaluations.  This makes me wonder if I am making the problem harder than it is and that there might be a better way already available.  So my questions are basically this: Does anyone know of methods for optimizing cost functions, convex or not, when evaluation is slow?  Or, am I doing something silly in the first place by rerunning the algorithm and comparing against the sample cohort so many times? Add an application to the command search path in csh Recently, I have installed an application (gnuplot) under user directory (/home/usr/bin). I want to run the application whenever I type 'gnuplot' in any directory. What could I do?  I tried to set the path in ~/.cshrc by  setenv gnuplot /home/usr/bin/gnuplot   but it doesn't work. It reports "command not found" as I type gnuplot in the terminal. I own a 2016 Macbook (with the USB-C charging) - at the time and in response to all of the reports of poor cables and poor chargers, I bought a meter so I could see what the throughput of my cables/chargers was. However, having run some tests I'm now not sure what to consider normal / what is harmless to the battery.   For all tests I used an original Apple C-C cable - though was able to replicate with two third party cables I own.  I have the original Apple block charging at 14.3 V / 1.99 A and a third party block that charges the same.  Another third party block which advertises USB PD and 3 A is currently charging at 20 V / 1.43 A  I've done some research online but I can't find any articles that indicate what a normal USB PD output is relative to the devices that connect to it and would appreciate any guidance / assistance.   TL;DR: Have Apple charger which charges at one voltage/amperage. Bought several others advertised at PD which are higher voltage, lower amperage. Not sure what is 'safe', or 'fast', or does least overall damage to battery. Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$ Suppose $f$ is continuous and periodic on the reals with period 1. Prove that if $x\in[0,1]$ is an irrational number, then  $$\lim_{N\rightarrow\infty}\frac{1}{N}\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$$   Suggestion: First consider $f(t) = e^{2\pi(ikt)}$ where k is an integer.   I can see that this is a limit of a weighted average, but the suggestion throws me off. I've seen the suggestion in fourier transforms but it's not clicking at the moment. Any help would be welcome. I am trying to create a beamer animation using tikz, but I can't even get basic rotating of a tikz image working as desired.  I have a rectangle specified by  \draw[rounded corners,dotted] (-3.5,0) rectangle (-0.5,2);   I would like to rotate this rectangle about the point (-1,.5) (which is near the bottom right corner of the rectangle).  I've tried:  {\rotatebox[origin=c,x=-1,y=.5]{130}{             \draw[rounded corners,dotted] (-3.5,0) rectangle (-0.5,2);}}   But this produces an error.  If I just use the origin=c option, it compiles, but it rotates the rectangle about the point (0,0).  I've also tried it with just the x=-1,y=.5 (without the origin option), and it fails to compile.  I have searched the documentation, which is where I learned about the options x=xdim and y=ydim.  However, I can't find a single example demonstrating how these options should be used.  Any suggestions would be greatly appreciated.    Also, if there is a better command for rotating things that will be more suitable for use in a beamer animation, please let me know.  Thanks! Which tables are safe to clear? How do I remove a property from a JavaScript object? Internal or external oscillator I always use the internal oscillator that pics have as I have never found the need to run anything at higher frequency than 8 MHz (which is the fastest the pics I use tend to be able to go). Are there any reasons, beyond going above 8 MHz, that mean I should use an external oscillator? It just seems like one more thing to go wrong to me but I'd be interested to hear what others do. What are the key principles that effective designs share? You have arrived on this page because you are clearly curious about underlying fundamentals that you can incorporate into your thought process when designing.  According to many that came before us, there are key principles that can be considered when creating an effective design. In the following answers, you will find useful theories from a variety of respected sources.  Use this question as a reference for navigating the variety of topics:  Gestalt Principles  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  Other Fundamentals and Useful Information  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  &nbsp;&nbsp;  If you know of a topic that hasn't been covered here, please add an answer with references to respected resources and it will be added to the list.  Of course direct quotes and paraphrasing from respected resources are a must, but should be limited to a small paragraph per topic at most and referenced back to their source as thoroughly as possible.  A  has been posted before, but not to create a collection of snippets that are enlightening for graphic designers of any and all skill levels. CUDA writing to constant memory wrong value If $x_1,x_2,\ldots,x_n$ are the roots for $1+x+x^2+\ldots+x^n=0$, find the value of $\frac{1}{x_1-1}+\frac{1}{x_2-1}+\ldots+\frac{1}{x_n-1}$ In Windows I used command-line clipboard copy-and-paste utilities...      pclip.exe and gclip.exe     These were UnixUtils ports for Windows (but they only handled plain text). There were a couple of other native Windows utilities which could write/extract any format.    I've looked for something similar in Synaptic Package Manager, but I can't find anything.    Is there something there, that I've missed? ... or maybe this is available in Bash scripting?    The type of utility I'd like will be able to read/write via std-in/std-out or file-in/file-out, and handle Unicode, Rich Text Format, picture, etc. clipboard formats...    NB: I'm not after a clipboard manager. Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$. Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.  So $(a^2+b^2)(c^2+d^2) = a^2c^2+a^2d^2+b^2c^2+b^2d^2$  and $(ac+bd)^2 = a^2c^2+2acbd+b^2d^2$  So the problem is reduced to proving that $a^2d^2+b^2c^2\ge2acbd$ but I am not sure how to show that I have an unusual problem with Chrome when I try to open PDFs. If I have already downloaded a PDF and try to download it again, I can open it by tapping its name; in the screenshot below, I could tap "pdf.pdf" to open the file.   The issue is that tapping this link actually opens RollerCoaster Tycoon Classic! If I choose to download again, Chrome redownloads and opens the PDF correctly, so it's not a huge issue, but still an inconvenience.  In Settings, it says that RollerCoaster Tycoon Classic has no defaults, and I am unable to change the "open supported links" setting.    How do I stop RollerCoaster Tycoon  trying to be a PDF reader? How to get to the GRUB menu at boot-time? In the textbook, it said a wave in the form $y(x, t) = A\cos(\omega t + \beta x + \varphi)$ propagates along negative $x$ direction and $y(x, t) = A\cos(\omega t - \beta x + \varphi)$ propagates along positive $x$ direction. This statement looks really confusing because when it says the wave is propagating along $\pm$ x direction, to my understanding, we can drop the time term and ignore the initial phase $\varphi$ while analyzing the direction, i.e. $y(x, 0) = A\cos(\pm\beta x)$, however, because of the symmetry of the cosine function, $\cos(\beta x)\equiv \cos(-\beta x)$, so how can we determine the direction of propagation from that?  I know my reasoning must be incorrect but I don't know how to determine the direction. So if we don't go over the math, how to figure out the direction of propagation from the physical point of view? Why $-\beta x$ corresponding to the propagation on positive x direction but not the opposite? Official reasons for "Software caused connection abort: socket write error"