Counter examples in group theory
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
How to call gdal_translate from Python code? Is it possible to use some gdal API to call gdal_translate from Python code? I do not mean simply executing the gdal_translate.exe from the file system, but rather call it somehow in code so I do not need to know the exact directory the gdal_translate executable is in? Reading Excel files from C# Is it possible to switch from one area of graduate study to another in US universities? For example, suppose someone has enrolled in a computer science phd program. Can he switch over to math(or physics) phd program in the same school later?(or say from applied mathematics to pure mathematics?)  What are the steps for doing for doing that? Is there a limit of $\cos(n!)$? I encountered a problem today to prove that $(X_n)$ with $X_n = \cos(n!)$ does not have a limit (when $n$ approaches infinity). I have no idea how to do it formally. Could someone help? The simpler the proof (by that I mean less complex theorems are used) the better. Thanks Adapt Ubuntu to a high-DPI resolution screen How can I adapt Ubuntu to a high resolution display?  I have a display with 3200x1600px on only 11'' and everything looks really tiny. Resize images in PHP without using third-party libraries? Add notes under the table I'm using the latex package  because the  package isn't using APA style version 6 yet.  Now I'm trying to add a table with notes right underneath it, like in this table for instance:    Since the \caption{} is used as a title above the table, I have to add an extra row for the notes that goes over the whole table width. The problem is that the notes won't fit into one line so I need multi-line cell. How can I accomplish that? Or am I doing it totally wrong and there is a much easier way? I guess footnotes don't work here.  \documentclass{apa6e}  \begin{document} \shorttitle{} \begin{table} \caption{title} \begin{tabular}{cc} foo &amp; bar\\ \hline \multicolumn{2}{l}{Notes. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Cras lacus orci, porttitor et posuere sit amet, tempor non justo. Ut quis aliquet turpis. Ut dictum nulla eget purus elementum a lacinia libero varius. Donec malesuada nulla ut odio rhoncus convallis. Aenean faucibus sollicitudin sapien, a vestibulum ante rhoncus sit amet. In vitae mi justo. In arcu metus, porta et lacinia ut, ultricies sed eros.} \end{tabular}  \end{table} \end{document} Should words be capitalized for being religious terms? While googling about whether "atheist" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across    It says     [Capitalize] Religions and religious terms       Examples:      Catholicism, Hinduism, Buddha, the Bible, Christian, the Ten   Commandments, Baptist church, Mt. Zion Methodist Church      NOTE: Do not capitalize the following:       Examples:      church, communion, atheist, agnostic, spirituality   but I don't recall hearing of such a prescription before. Wouldn't most of the examples listed be capitalized because they're proper nouns? Are there good examples of words being capitalized solely because they're religious terms?  I'm mainly interested in modern English, rather than days of past where a lot more words were capitalized than they are nowadays.  Somewhat related:  - use "God" when referring to the name of the god of Judaism and Christianity (a proper noun), but "god" when referring to the general concept of a deity (common noun). Can “due to” and “because of ” be used interchangeably? Is it fine to use due to in place of because of ? How about the other way around? Are any of these sentences ungrammatical?   He was lost because of the storm. He was lost due to the storm. He lost his way due to the storm. He  lost his way because of the storm. Distance between surfaces mixed declarations and codes Let $G=\langle a\rangle$ be a cyclic group of order $n$. Show that, for every divisor $d$ of $n$, there exists a subgroup of $G$ whose order is $d$. I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) Is there any way to do n-level nested loops in Java? In other words, can I do something like  for() {     for {        for {        }     } }   Except N times? In other words, when the method creating the loops is called, it is given some parameter N, and the method would then create N of these loops nested one in another?  Of course, the idea is that there should be an "easy" or "the usual" way of doing it. I already have an idea for a very complicated one. When using processing tool in pyqgis and run, it always creates a progress bar. Is there a way to disable it?  processing.runalg('qgis:fixeddistancebuffer', _layer, distance_tolerance, 10, False, None)   I want to disable it because I get this error when I run my script in travis:     wrapped C/C++ object of type QProgressBar has been deleted See log for   more details       RuntimeError: wrapped C/C++ object of type QProgressBar has been   deleted Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference. Given a sphere of radius $r$ with two spherical caps on it defined by the radii ($a_1$ and $a_2$) of the bases of the spherical caps, given a separation of the two spherical caps by angle $\theta$, how do you calculate the surface area of that intersection?   To clarify, the area is that of the curved surface on the sphere defined by the intersection. At the extreme where both $a_1,a_2 = r$, we would be describing a spherical lune.   Alternatively define the spherical caps by the angles  $\Phi_1 = \arcsin(a_1/r)$ and $\Phi_2 = \arcsin(a_2/r)$. Load a table with NO geometry_column using PyQGIS What is a race condition? When writing multithreaded applications, one of the most common problems experienced is race conditions.    My questions to the community are:  What is the race condition? How do you detect them? How do you handle them? Finally, how do you prevent them from occurring? Why doesn't Ubuntu 16.04 in Windows have ubuntu.exe?