NDSolve with NIntegrate
How to plot and solve the numerical solution of a integro-differential equation
Capture console exit C# Array only adds duplicate values Batch files: How to read a file? Property of Entire Functions Suppose $f$ and $g$ are entire functions with $|f(z)|\leq|g(z)|$ for all $z$.  How can we show that $f=cg$ for some complex constant $c$?  Thanks for any help :) Intersecting transparent object causing artifacts in cycles When two objects -one of them transparent- intersects it creates some artifacts visible even in the alpha channel. Even with 1024 transparent bounces the artifacts remain.    In the example file there are two cubes in the same position, one transparent and one emission.    What is causing this? Any way to get rid of this artifacts? Why is triple-DES using three different keys vulnerable to a meet-in-the-middle-attack? Among other sources,  states that triple DES using three seperate keys (k1, k2, k3) is vulnerable to meet-in-the-middle-attacks, while triple DES using only two keys (k1, k2, k1) is not.  Why is this attack possible if all the keys are different, but not if the first and the third are the same? Your UK visa application has been issued.      PLEASE DO NOT GO TO THE VISA APPLICATION CENTRE BEFORE THEY CONTACT YOU.      You will be contacted by the Visa Application Centre when your documents are ready for collection, or have been dispatched via courier where this is relevant.       You are reminded that you should avoid making travel plans until you have collected your passport, as the outcome of your visa application is not final until you receive your passport.      Please ensure you check the details on your visa when collecting your passport. If you need to contact us you can do so via our International Enquiry Service at www.gov.uk/contact-ukvi-outside-uk      Kind regards,      UK Visas and Immigration   British Embassy Abu Dhabi     Your UK visa application has been issued.   I know words like processed, forwarded, received, refused but never heard anything like that, so I am confused. Language hints for quoted code In  I tried to add  for syntax formatting to code blocks quoted from the question. However, it seems they won't be honoured if I write them as a comment in my own part of the post, and if I include the hint in the qutotation as well then I have some ugly empty space before the code block. There should be a way to write these things properly. I have a simple question answer to which would help me more deeply understand the concept of (non)commutative structures. Let's take for example (our teacher's definition of) a ring:  Let $R\neq \emptyset$ be a set, let $\oplus:A\times A \to A$ and $\bullet :A\times A \to A$ be binary operations. Moreover, let $(R, \oplus)$ be a commutative group, $(R, \bullet)$ be a monoid and following property holds for all $a, b, c\in R$: $$a\bullet(b\oplus c) = (a\bullet b)\oplus(a \bullet c)$$ $$(b\oplus c)\bullet a = (b\bullet a)\oplus(c \bullet a)$$ Then ordered triple $\mathbf R = (R, \oplus, \bullet \mathbf)$ is called a (unitary) ring.  Moreover, we call ring $\mathbf R$ commutative iff $(R, \bullet)$ is a commutative monoid. Commutativity of a ring is always a matter of its multiplicative operation because the additive operation is always assumed to be commutative.  Could anyone explain me the bold part? Why do we even in non-commutative rings (and fields etc.) assume the addition to be always commutative? Is there some serious reason? Would it make any trouble? Or studying of structures with non-commutative addition just doesn't give us anything new so we can take addition as commutative simply because of our comfort? Finding CPU usage of a service Because my laptop fan was spinning up for no reason, I had a look at the CPU usage and I see  svchost with 12.5% CPU, which is basically a full core.  Now, I'm aware that  svchost runs services and I know how to display the services it runs in Task Manager or Process Explorer ().  Now I know which services are run, but I don't know which service eats the CPU time. I could disable one service after another, but I don't really like doing this (it could break things that are currently in use and I could forget turning the service back on later).  Therefore I'd like to know whether it's possible to instruct Windows to run only one service per svchost the next time I boot my PC. While I might have the slight disadvantage of several processes, I could immediately find out which one it is and it would be a much easier decision of whether or not to stop or restart the service. "matrix is not positive definite" - even when highly correlated variables are removed The following code receives seg fault on line 2:  char *str = "string"; str[0] = 'z';  // could be also written as *str = 'z' printf("%s\n", str);   While this works perfectly well:  char str[] = "string"; str[0] = 'z'; printf("%s\n", str);   Tested with MSVC and GCC. "inputenc Error: Unicode char \u8" error while trying to write a degree symbol (invisible character) No matter how I try to do it I always get the following error :      ! Package inputenc Error: Unicode char \u8:­ not set up for use with LaTeX.    I have tried using ­­­$^{\circ}$, \deg, \textdegree, pasting the ° symbol directly, to no avail.  Here is the header of my document, in case one of those could be causing the errors :  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage[francais]{babel} %\FrenchItemizeSpacingfalse \frenchbsetup{CompactItemize=false} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amsthm} Number of solutions of an arithmetic function's equation Say, an equation is given below \begin{equation} 2\pi(x) - \pi(2x)=\omega(x) \end{equation}  where $x$ is a positive integer, $\pi(x)$ is the prime-counting function, and $\omega(x)$ is the number of distinct prime factors of $x$.  I would like to know if this equation holds for finitely many values of $x$ or infinitely many.  If one uses asymptotic formula (from number theory) it can be written that \begin{equation} \omega(x) \sim \ln x / \ln \ln(x) \end{equation} (from )  and  \begin{equation} \pi(x) \sim x/\ln(x), \end{equation} so the above equation can be rewritten (after simplification) as \begin{equation} 2x\ln(2)=\ln(x)\ln\ln(x)\ln(2x) +f(x) \end{equation}  where $f(x)$ is an error term.  If  I plot left side (which is linear, supposed to be a straight line) and right side(a curve),assuming $ f(x) $ is 100% accurate, then the equation implies(?!) that the right will intersect left side. Since line can intersect a curve ($ln  $ function) finite times, so there are finite intersection point. So, can I say that there are only finitely many values of $x$?  graph example-   here f(x) is assumed as x + sinx  without the f(x)- If I close (is delete an option ?) my Gmail account, will somebody be able to register using my email address and read my mails?  I want to close my Gmail account but I don't want anybody to impersonate me with my old address.  Same question with Yahoo! Mail. Do they allow addresses to be re-used? I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice water mixture comes crashing down. With my open mouth overfilled with ice water, my shirt gets wet – I hate when this happens. After drying myself off, I started thinking why this does happen:   How does ice that starts off loose and separated in water fuse together to form one large clump? What causes the ice-water mixture to stop flowing momentarily and then suddenly starting flowing again? Is it that the ice fuses together in the glass and forms one large clump, and then the friction with the edges builds a "dam-like" situation? Or are there individual pieces of ice fusing with the edges of the drinking glass damming-up the ice? Better explanation of the common general relativity illustration (stretched sheet of fabric) Initial note: Having read , the answers there do not help in this specific situation, as they rely on having lots space to spare - I have very little.  When I started my city, I designed a simple exit from the default highway that I thought was sustainable: I left enough space around it to upgrade the road as I needed to, which has worked up until now. However, I am now stuck with a six-lane one-way exit from the highway that isn't getting used: since cars seem to pick the most efficient lane to get where they want to go, regardless of traffic, the rightmost lane fills up, then spills over onto the highway. This blocks the highway, my bus routes, and more importantly my planned emergency routes.  My setup looks like this:    The red arrows show road direction, and the orange line is the traffic backed up. Note that in this image, I have replaced the six-lane one-way exit with a highway exit, as this is just about as efficient...  This situation is getting to be pretty bad, and is bringing half my city to a standstill. Its effects compound themselves further down the highway:    In this image, the orange line is the traffic directly caused by this exit not working. This traffic jam then blocks two exits/entrances further down, on the red crosses; the yellow line shows the traffic jam caused by these being blocked. In other words, my inefficient exit design is now blocking itself from moving.  So this is a two part problem.   Considering that I'm constructing a residential district in the space above left of the problem exit, and would like to keep the solution inside the power line, how can I redesign this exit to be more efficient? How do I solve the ring of traffic jams? Is it a simple case of just deleting and replacing a bit of road? I've read a lot of conflicting advice on whether it's advisable to store eggs in the refrigerator. The case against seems twofold: (1) that eggshells are porous, and eggs can take on unwelcome flavours, or even spoil faster in the fridge, and (2) that cooking with cold eggs can be problematic. But lots of people refrigerate eggs through perceived necessity.  Do eggs last longer in the fridge, and is the shelf life gain worth it? Or should I just stick them in the cupboard? Background:   Story: A colleague of mine told me about  and it seems good to me. I am always trying to use tools which Mac OS X itself gives me, so I've given the Keychain a try. It seems satisfying, but I don't know how to tell Google Chrome to use my specific keychain. I need it to separate saved stuff for work and for private (syncing private to work, but separated from work data).  Stuff:   Google Chrome 21.0.1180.57 (Fully updated) Mac OS X Lion (Fully updated) OS X Mountain Lion (Fully updated)   Question:  How do I tell to Chrome to use a specific keychain and to save data from/to this keychain?