How to find indices of groups in JavaScript regular expressions match?
Get index of each capture in a JavaScript regex
Heroku and Twisted Are there any examples of $\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$? I am writing a short discussion of Farey numbers and was wondering if there are any examples of when the mediant function is ever actually equal to the sum of the two fractions in the usual sense? (Not to produce Farey numbers, I just thought it might be an amusing way to introduce Farey addition).   Explicitly: Are there any examples of fractions $\frac{a}{b}$ and $\frac{c}{d}$ where  $$\frac{a}{b}+\frac{c}{d}=\frac{a+c}{b+d}$$ for positive integers?   Currently I have found the example  $$\frac{1}{1}+\frac{1}{i} =\frac{1+1}{1+i}$$ if we remove the integers requirement but it would be nice to find a case that didn't involve complex numbers though! Asking the position of a person in a sequence Why does every server I try say it can't connect? I just re-purchased Minecraft (because my old profile stopped working so I bought it) after not playing it for a couple of months. I've added a bunch of servers, but almost every one says "can not connect."  I know its not because the server is not 1.7.2, because I checked that they'd update. It will say "server can't connect" after a long time. I don't know if its me or the servers.  My server screen looks like this (notice the one at the bottom – it's still loading!): After burning Ubuntu 12.04 to a CD, I tried booting and got the message:  This kernel requires the following features not present on the CPU: pae  Unable to boot - please use a kernel appropriate for your CPU.   What does this mean? What does "cpu MHz" field mean in the /proc/cpuinfo of a hyper-threading cpu? The CPU is a i7-3770@3.40GHz. It has 4 cores and each core has 2 threads. Here is the dmidecode output:  # dmidecode -t 4 # dmidecode 2.9 SMBIOS 2.7 present.  Handle 0x0042, DMI type 4, 42 bytes Processor Information     Socket Designation: SOCKET 0     Type: Central Processor     Family: &lt;OUT OF SPEC&gt;     Manufacturer: Intel(R) Corporation     ID: A9 06 03 00 FF FB EB BF     Version: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz     Voltage: 1.1 V     External Clock: 100 MHz     Max Speed: 3800 MHz     Current Speed: 3400 MHz     Status: Populated, Enabled     Upgrade: &lt;OUT OF SPEC&gt;     L1 Cache Handle: 0x003F     L2 Cache Handle: 0x003E     L3 Cache Handle: 0x0040     Serial Number: Not Specified     Asset Tag: Fill By OEM     Part Number: Fill By OEM     Core Count: 4     Core Enabled: 4     Thread Count: 8     Characteristics:         64-bit capable   It will be 8 logic core in a system, like what shows in /proc/cpuinfo. But can any one tell why the cpu MHz of a core is 1600MHz? I guess there is 2 threads in a core, so a hw thread freq may be about the half of the core's? How this number is calculated?  processor   : 7 vendor_id   : GenuineIntel cpu family  : 6 model       : 58 model name  : Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz stepping    : 9 cpu MHz     : 1600.000 cache size  : 8192 KB physical id : 0 siblings    : 8 core id     : 3 cpu cores   : 4 apicid      : 7 initial apicid  : 7 fpu     : yes fpu_exception   : yes cpuid level : 13 wp      : yes flags       : fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx rdtscp lm constant_tsc arch_perfmon pebs bts rep_good xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat tpr_shadow vnmi flexpriority ept vpid bogomips    : 7013.49 clflush size    : 64 cache_alignment : 64 address sizes   : 36 bits physical, 48 bits virtual power management:   Also, here is the output of lshw and lscpu command. There are also 1600MHz mentioned.   lshw info:  #lshw -class processor   *-cpu                           description: CPU        product: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz        vendor: Intel Corp.        physical id: 42        bus info: cpu@0        version: Intel(R) Core(TM) i7-3770 CPU @ 3.40GHz        slot: SOCKET 0        size: 1600MHz        capacity: 3800MHz        width: 64 bits        clock: 100MHz        capabilities: fpu fpu_exception wp vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx rdtscp x86-64 constant_tsc arch_perfmon pebs bts rep_good xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat tpr_shadow vnmi flexpriority ept vpid cpufreq   lscpu info:  #lscpu Architecture:          x86_64 CPU op-mode(s):        32-bit, 64-bit CPU(s):                8 Thread(s) per core:    2 Core(s) per socket:    4 CPU socket(s):         1 NUMA node(s):          1 Vendor ID:             GenuineIntel CPU family:            6 Model:                 58 Stepping:              9 CPU MHz:               1600.000 Virtualization:        VT-x L1d cache:             32K L1i cache:             32K L2 cache:              256K L3 cache:              8192K Why do some bad traits evolve, and good ones don't? If a trait would be advantageous to an organism then why hasn't it evolved yet?  Conversely, if a trait is not advantageous or mildly disadvantageous, why does it exist?  In other words why does evolution not make the organism more "perfect"?    This is a general question that would be applicable for any kind of trait. Please keep the answers precise and scientific.   Read this meta post for more information: Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$ Find whether the integral converges or diverges. $$\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$$  I simplified it to $$\int_{0}^{1}\frac{\log(x)}{(1-x)(1+x)}dx$$  Here I have $2$ "bad" bounds (both $0$ and $1$).  I think, to prove such integral converges, I should find something that is equivalent to or less than $\log(x)$ so I can exchange them, maybe $\sqrt{x}$, so it may cancel out the fraction, and I can compare it to $$\int_{0}^{1}\frac{dx}{x^p}$$  Also I had an idea to substitute $x$ with $u+1$ so I can use $\log(1+u) \sim  u$ when $u \rightarrow 0$. I'm allowed(not familiar with anything else) to use direct comparision test, limit comparision test, Cauchy test and Abel-Dirichlet's test.   Any hints are much appreciated, I just want to get the big picture.   Thank you. My system was configured to dual boot Ubuntu 12.04.1 LTS and Windows 7. Today I got my hands on the MSDN release of Windows 8 and I installed it over my Windows 7. Now the computer just boots to Windows 8 directly without loading the GRUB screen.  So I followed the steps as suggested in: . Running this command:      ls -l /dev/disk/by-label/   gives the following output:      total 0     lrwxrwxrwx 1 root root 10 Sep 11 07:51 Entertainment -&gt; ../../sda2     lrwxrwxrwx 1 root root 10 Sep 11 02:45 PENDRIVE -&gt; ../../sdb1   Also fdisk -l command gives this as the output:      Disk /dev/sda: 320.1 GB, 320072933376 bytes     255 heads, 63 sectors/track, 38913 cylinders, total 625142448 sectors     Units = sectors of 1 * 512 = 512 bytes     Sector size (logical/physical): 512 bytes / 512 bytes     I/O size (minimum/optimal): 512 bytes / 512 bytes     Disk identifier: 0x1246aa23         Device Boot      Start         End      Blocks   Id  System     /dev/sda1   *        2048   319582199   159790076    7  HPFS/NTFS/exFAT     /dev/sda2       319582208   602906623   141662208    7  HPFS/NTFS/exFAT     /dev/sda3       602908672   625135615    11113472   83  Linux      Disk /dev/sdb: 1939 MB, 1939865600 bytes     64 heads, 63 sectors/track, 939 cylinders, total 3788800 sectors     Units = sectors of 1 * 512 = 512 bytes     Sector size (logical/physical): 512 bytes / 512 bytes     I/O size (minimum/optimal): 512 bytes / 512 bytes     Disk identifier: 0xc3072e18         Device Boot      Start         End      Blocks   Id  System     /dev/sdb1   *        2248     3788799     1893276    c  W95 FAT32 (LBA)   So I assume that I have to run this: sudo grub-install /dev/sda3 to get GRUB up and running. But I am getting this error:      /usr/sbin/grub-probe: error: cannot find a device for /boot/grub (is /dev mounted?).   Can anyone please guide me in the right direction? The current Ubuntu installation is far too customized to my needs to lose it to a boot manager issue! Any help is much appreciated! While editing some ad copy, and I was given the sentence, "Defending a lawsuit can be a big cost for your business." (My italics.)  I keep thinking the proper word to use is "expense" rather than "cost" as in: "Defending a lawsuit can be a big expense for your business." But I'm just not sure I'm correct.   Can anyone help with more definitive guidance? Can "cost" and "expense" be used interchangeably in a sentence like this?   Thank you! What should I do when I see a "question ban warning"? When I  question, It says following:     Wait! Some of your past questions have not been well-received, and   you're in danger of being blocked from asking any more.      For help formulating a clear, useful question, see: How do I ask a   good question?      Also, edit your previous questions to improve formatting and clarity.   Here is screen-shot:   So, What should I do? (How long to wait?) I am currently learning how to use TikZ/PGF to make some figures for a project report, and so I have a question:     Is there is a practical way of making a particular object into a node?   The object I have in mind is shown in the Figure below. I want the object to consist in the big circle, the two circular arcs, the label and anchors at north, south, east and west. The dotted lines are simply there to indicate that I am going to have paths going out of these points, which is why I need the anchors there.     I include the source, in the case that it is useful to anyone.  \begin{tikzpicture} \draw[help lines, gray, dotted] (-2,-2) grid (2,2);  \begin{scope}[shift={ (0,0) } ]     \begin{scope}[rotate=90]         \draw[thick] (-1,0) arc[start angle=-90, delta angle=90, %                               x radius=1, y radius=1] -- (0,1) %NW                      (0,-1) arc[start angle=180, delta angle=-90, %                                    x radius=1, y radius=1] -- (1,0); %SE         \draw[gray] (0,0) circle (1);     \end{scope} % Anchor replacements     \node(N1)       at (0,1)    {};     \node(S1)       at (0,-1)   {};     \node(E1)       at (1,0)    {};     \node(W1)       at (-1,0)   {}; % Label     \node(Crossing number) at (0,0) {1}; \end{scope}  \path[thick, gray, dotted] [ out=90,   in=270]     (N1.center) edge (0,2) [ out=180,  in=0]       (W1.center) edge (-2,0) [ out=270,  in=90]      (S1.center) edge (0,-2) [ out=360,  in=180]     (E1.center) edge (2,0); \end{tikzpicture}   PS. I have had a look at the Manual, but I could not find a description of how to do this. Exponent and abelian groups What exponent $e$ can guarantee the group to be abelian? Are there any known results except the case $e = 2$? Thanks for help. When a polished piece of metal (or steel in particular) is heated to incandescence, how do its reflective properties change?  Given a mirror-like surface, would the object temporarily cease to act like a mirror at a certain temperature?  Would the specular reflection of light turn into diffuse reflection; in other words, would the surface temporarily become matte/dull?  I am not asking about permanent changes to the object such as melting, but rather can there be a temporary change in the reflectivity only while the the object is hot, that disappears when the object is cooled down?  Background of the question: I have a laser scanner that usually has trouble scanning shiny surfaces with high specular/ low diffuse reflectivity; and it seems to work a lot better for hot steel pieces than for cold ones. Glowing steel also looks less shiny to me than cold steel, but of course that is hard to tell with all the glowing This is what happens:  sudo apt-get install vlc Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package vlc   Please help. I would also like to know when this error occurs, I've seen it before too. Is there anything beyond subtle hints that Jack becomes the Face of Boe? Way to list "Contact Us" email address on web site, yet reduce likelihood of spam? Using article published dates effects SEO? In my blog I publish articles with date below under it.  My questions are:   Using dates will have positive impact or negative impact? After few years of publishing the post, since my post age is old will it remain in same position of search results or it will go down? Finally, should I use published dates or not? How to completely uninstall and remove QGIS 2.8.1 on Windows Vista? I want to uninstall and completely remove QGIS installation from my computer(windows vista). I have uninstalled it and when i try to reinstall it says it is already installed on the system.