I have two Strings, str1 and str2. How do I check if str2 is contained within str1, ignoring case?

Say I have two strings,  String s1 = "AbBaCca"; String s2 = "bac";   I want to perform a check returning that s2 is contained within s1. I can do this with:  return s1.contains(s2);   I am pretty sure that contains() is case sensitive, however I can't determine this for sure from reading the documentation. If it is then I suppose my best method would be something like:  return s1.toLowerCase().contains(s2.toLowerCase());   All this aside, is there another (possibly better) way to accomplish this without caring about case-sensitivity?


This is my first attempt to code in Python.   I have one polygon layer, A, that covers the UK and another set/group of layers that each cover sections of the UK, B. I want to select by location features of A contained entirely within B. As B is split into lots of separate sections (due to its size) I need to do this in a loop.   So far I have this code which I adapted from a similar question of :  # Import system modules import sys, string, os, arcgisscripting, arcpy  # Create the Geoprocessor object gp = arcgisscripting.create()  mxd = arcpy.mapping.MapDocument("CURRENT") df = mxd.activeDataFrame groupName = "WBBS_waterways"  # Load required toolboxes... gp.AddToolbox("c:/program files (x86)/arcgis/desktop10.3/ArcToolbox/Toolboxes/Data Management Tools.tbx")  # Script arguments... A = "//FILES/UNIXHome/Git/waterbirds_project/data/OS_waterways.shp" outfolder ="//FILES/UNIXHome/Git/waterbirds_project/data/"   basename = "OS_just_rivers"  allLayers = arcpy.mapping.ListLayers(mxd, groupName, df)[0]  for layer in(allLayers):         print("A")         D=layer.name         # Process: Select Layer By Location...         gp.SelectLayerByLocation_management(A, "COMPLETELY_WITHIN", D, "", "NEW_SELECTION")         print("B")         outname = outfolder + "\\" + basename + D         print("C")         #Process: Copy Features...         gp.CopyFeatures_management(A, outname, "", "0", "0", "0")    And this is the error message I get:  Runtime error  Traceback (most recent call last):   File "<string>", line 28, in <module> ExecuteError: ERROR 000368: Invalid input data.     which I think means something is going wrong on this line: gp.SelectLayerByLocation_management(A, "COMPLETELY_WITHIN", D, "", "NEW_SELECTION"), it looks like python can't find layer D but I'm not sure how to make it recognise layer D.

I am attempting to iterate over all the feature classes in a folder and I'm getting the error 000368. The other solutions in on SE were not helpful to me unfortunately, so I'm posting a separate question. search_grids is a list of point feature classes and searches is a another point feature class.   The points never actually intersect with each other, but I'm using the Select by location tool to select points within a specified distance of each other. This isn't the reason for the error though as I was able to get this to work in the python window in ArcMap.   My code is the following  arcpy.env.workspace = r"C:\workspace" search_grids = arcpy.ListFeatureClasses() searches = r"C:\workspace\search" for grid in search_grids:     arcpy.management.SelectLayerByLocation(grid,"INTERSECT",searches,"97.5 meters","NEW_SELECTION","INVERT")     arcpy.management.SelectLayerByLocation(grid,"INTERSECT",searches,"2.5 meters","ADD_TO_SELECTION","NOT_INVERT")   Why am I getting this error?       arcgisscripting.ExecuteError: Failed to execute. Parameters are not valid.   ERROR 000368: Invalid input data.   Failed to execute (SelectLayerByLocation)


I m trying to install zoom on ubuntu, doing thru graphic installer did not work, i tried thru terminal with 'sudo apt-get install ./zoom-package'  and it gave me this error:  the following packages have unmet dependencies:  zoom : Depends: libxcb-xtest0 but it is not installable E: Unable to correct problems, you have held broken packages   i did  sudo apt-get autoremove   still did not work. any ideas?

There are now errors when updating and I cannot install most software due to a corrupted  /etc/apt/sources.list   file. Is there a copy I can download to replace it?  The file would be for Ubuntu 12.04 (Final Beta) in the United States.


I really want to install  to my minecraft. Its an adventure map. I have looked at several youtube videos on how to install it but they all say the same thing, once I get to the "go to the saves folder" i get stuck cause in my minecraft i dont have a saves folder :( I found the hidden Library, and searched for my minecraft folder, but there isn't a saves folder inside. I'm on a Macbook Air, OS X Version 10.9.  What can I do so I can install this?

I want to copy/modify/delete a Minecraft world. Where can I find my saves folder?


I am trying to prepare a few of my images for printing purpose. I have never printed images before, so this is my first time.  Most of my pictures are taken by a drone. The resolution says 3000x4000, with 300 ppi. I have edited  it in photoshop, added a layer for high pass filter and exported it as a jpeg with 100% quality.  However, when I open the exported jpeg file, and go to its properties, it says horizontal resolution 96 dpi and vertical resolution 96 dpi. I don't know why this is happening and I am confused. Can someone please help?

I often see statements in discussions about web displayed image quality that go something like this: "I only upload pictures at 72 dpi and 1200 pixels on the long edge, so if someone copies and prints the image it won't look as good as if it were 300 dpi."  What? Have I missed something here?  Does an image edited and saved/exported with 1200x800 pixels at 300 ppi look any different online than the same image saved/exported with 1200x800 pixels at 72 ppi? Other than the metadata regarding ppi, is there any difference in the two images at all? If so, what is the difference? If I tell my printer to print the images at 4R (4X6 inches) will there be any difference at all in how the printer creates a print from the 1200x800 @ 300 dpi image versus the 1200x800 @ 72 dpi image?


Suppose that $e$ is the identity in a group G and that $a^2 = e $ for all $a\in G$. Show that G is abelian.  How do I figure out what the binary operation is to show that G is abelian i.e. if this is the correct line of thought in the first place. If not, i require some assistance.

Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian.   This question is from group theory in Abstract Algebra and no matter how many times my lecturer teaches it for some reason I can't seem to crack it.   (Please note that $e$ in the question is the group's identity.)  Here's my attempt though...  First I understand Abelian means that if $g_1$ and $g_2$ are elements of a group $G$ then they are Abelian if $g_1g_2=g_2g_1$...  So, I begin by trying to play around with the elements of the group based on their definition...  $$(g_2g_1)^r=e$$  $$(g_2g_1g_2g_2^{-1})^r=e$$ $$(g_2g_1g_2g_2^{-1}g_2g_1g_2g_2^{-1}...g_2g_1g_2g_2^{-1})=e$$  I assume that the $g_2^{-1}$'s and the $g_2$'s cancel out so that we end up with something like,  $$g_2(g_1g_2)^rg_2^{-1}=e$$ $$g_2^{-1}g_2(g_1g_2)^r=g_2^{-1}g_2$$  Then ultimately...  $$g_1g_2=e$$  I figure this is the answer. But I'm not totally sure. I always feel like I do too much in the pursuit of an answer when there's a simpler way.  Reference: Fraleigh p. 49 Question 4.38 in A First Course in Abstract Algebra.


Suppose we have two functions $f,g:\mathbb{R}\to{\mathbb{R}}$ such that: $$\lim_{x\to{}\alpha}{f(x)}=L \text{ and }\lim_{y\to{\beta}}{g(y)}=\alpha.$$ Is then true that: $$\lim_{y\to{}\beta}{f(g(y))=L}?$$ My intuition tells me yes. Using an $\epsilon-\delta$ approach seems very long and tedious. Is that the case? Or is there a nice way of showing this to be true. Or, is there a nice counterexample?

Find functions $f,g : \mathbb R \longrightarrow \mathbb R $ and $a,b,c \in \mathbb R $ such that  $$ \lim_{x \rightarrow a} f(x) = b \quad \text{and} \quad \lim_{y \rightarrow b} g(y) = c \quad \text{but}\quad \lim_{x \rightarrow a} g(f(x)) \neq c$$  I tried to use non continous functions but i didnt manage to get a any useful results.


If $\alpha $ and $\beta$ are roots of equation $a\tan\theta +b \sec\theta=c$. Prove that $\tan(\alpha  + \beta)=\frac{2ac}{a^2-c^2}$  i have converted tan to sin and cos and reached to $\sin^2\theta(a^2-c^2+2ac) + c^2-b^2-ac=0$. how do i proceed  thanks

if $\alpha$ , $\beta$  are the values of  $\theta$ satisfying  $$\displaystyle a\tan(\theta)+b\sec(\theta) = c$$     prove that $$\displaystyle\tan(\alpha+\beta) = \dfrac{2ac}{a^2-c^2}$$ How do i solve this, suggestions about how to go about doing this


I've been wondering about the 'small' part of the attacks on RSA, like the small public key exponent and the small private key exponent and what's not really clear is how small are we talking about? Like is it how small with respect to the large prime numbers or what exactly?

Just to establish notation with respect to the RSA protocol, let $n = pq$ be the product of two large primes and let $e$ and $d$ be the public and private exponents, respectively ($e$ is the inverse of $d \bmod \varphi(n)$).  Given a plaintext message $m$, we obtain the ciphertext $c = m^e \bmod n$; we subsequently decrypt the ciphertext by calculating $c^d \bmod n$.  Suppose I'm trying to implement RSA on a device with low computational power, and these exponentiations take too long.  I decide to make my implementation run faster by choosing small values for $e$ and $d$ (e.g. in the tens or hundreds).    Are there efficient attacks against such an implementation?


How to proof that a graph of order $n$, $n\geq 2$ has two vertices of the same degree?

Any help would be appreciated.  If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree?


I have 3 input languages installed and it is very annoying to change them with standard Windows keys because I am often overflow the language.  I would prefer to improve this. One improvement would be to make switch like in Ubuntu, where Ctrl-Right Shift switches "right" and stop at the end of language list and Ctrl-Left Shift switches "left" and stop at the beginning of a list.  But I don't see it is possible.  Also, probably better behavior would be like Alt-Tab behavior.  Is it possible to improve?  UPDATE  I know how to set change shortcuts in Windows, the problem is that options are very poor:    Most of these combinations are used in many popular programs like Google Chrome, so they are unusable.  And in switch choice:    there is no way to disable cycling and palette is very poor. Actually I can choose between Ctrl-Shift and Alt-Shift.  I emphasize: the entire setting of language switch is nearly unusable in Windows. Most of options are conflicting with other programs and overall functionality is extremely poor.  So the question persists: how to set my own combination, not limited to this strange choice by MS? Or how to do something what I described in question?

Is there any way to set keyboard shortcuts to quickly change to a different language/keyboard layout? The old shortcuts still seem to work (when set back in Windows 7), but I can't seem to find anything to change it in Windows 10.


Which files I need to delete from the system of a rooted device to delete completely the recovery mode, and in which folder I can find them? Ty

Is there a way to disable recovery mode so it won't be possible to factory reset your phone?  Basically what I am trying to do, is that it should be impossible to factory reset the phone as there is no recovery partition.  (Example format the recovery partition, or hide the option of factory reset on the recovery menu, build a custom recovery etc.)  P.S.. I was thinking of maybe removing a system app (example package installer) and making it a user app, and therefore when you factory reset the phone it won't start cause the system app is missing, but when I tried that, the phone wouldn't start even without resetting it, as the system needs the system app to start, ( I thought that maybe even though I removed the app from being a system app, the phone would still start as it's still there as a user app, and only after resetting the phone - that the user apps get deleted, the phone won't start as it's missing the app).  Thanks in advance


I have strange thing happening in postgresql DB. I would like to understand what is the major difference between using st_equals and using the equals (=) sign ex :  SELECT * FROM x WHERE st_equals(the_geom, st_astext('POINT(962952.534 6469066.353)'));   and  SELECT * FROM x WHERE the_geom=st_astext('POINT(962952.534 6469066.353)');   An this code will not be the same as   SELECT * FROM x where st_geohash(st_transform(the_geom, 4326))=st_geohash(st_astext('POINT(962952.534 6469066.353)'));   and not even the same as   SELECT * FROM x WHERE st_astext(the_geom)=st_astext('POINT(962952.534 6469066.353)');   I would like to understand why the result of these request differ  EDIT: so this question was mark as duplicate, I didn't found this post about st_equals and equal sign at the time. About converting to text with st_astext I was thinking about losing precision may cause the difference. But about st_geohash ?

There are two methods of determining equality in PostGIS.   The equals operator     Obviously these two methods work different, but the docs on ST_Equals are not clear why,     Returns TRUE if the given Geometries are "spatially equal". Use this for a 'better' answer than '='. Note by spatially equal we mean ST_Within(A,B) = true and ST_Within(B,A) = true and also mean ordering of points can be different but represent the same geometry structure. To verify the order of points is consistent, use ST_OrderingEquals (it must be noted ST_OrderingEquals is a little more stringent than simply verifying order of points are the same).   This seems to mean there is two criterion for ST_Equals, and that is that   ST_Within(A,B) = true  ST_Within(B,A) = true   However, that ordering of points does not matter with ST_Equals. Presumably, that would matter with the equal operator then =? But, that doesn't match up with my observation.  So as three in the same questions..   What does the equal operator (=) do? What does the ST_Equals() do? What criteria does spatially equal include that = does not include?


I own an standalone DVR system (used for video surveillance) which apparently has an embedded Linux inside of it... The DVR writes the recordings on a locally attached SATA HDD.  Because I have no possibility to configure that embedded Linux to write the data to a NAS, I need to find some physical/hardware component to emulate a locally attached SATA HDD (as if a HDD were connected locally, but on the other side transmit the data over the LAN to my NAS like an iSCSI initiator...)  Does anyone know any hardware component for such a job?  Thanks!

Is there a USB WiFi dongle device that can:   Emulate a virtual mass storage device for a home video player But in fact shows the files from a network-shared folder?


If a man is standing on two weighing machines (scales), with one foot on each, Will both machines show equal weight or his weight will be distributed in two machines?

I frequent a blog from a British psychologist, and every Friday he likes to pose an interesting puzzle or riddle. The Monday after that he posts the answer. They're good fun, and IANAP but  made my it-might-not-be-quite-as-simple-as-that detector go off.  My question boils down to this: let's say I have two identical scales, and I stand on the scales with one foot on each scale. The scales read W1 and W2. Does my weight equal W1 + W2?


I have the following go code:  s := `prefix<b>Group ID:</b><br/> G123<br/>temporary<br/>suffix`  re := regexp.MustCompile(`(?s)(.*)<b>Group ID:</b><br/>(.*)<br/>(.*)`)  m := re.FindAllStringSubmatch(s, -1) fmt.Println(m[0][2])   playground link:   The above program prints \nG123
temporary because the last/second
 after the pattern is matched, as per the regex. Is there a way to get the first
 to be matched so that the output will be, just: G123. In addition to the first br match, the newline/whitespace in the beginning should also be stripped. Any suggestions ?

I have this gigantic ugly string: J0000000: Transaction A0001401 started on 8/22/2008 9:49:29 AM J0000010: Project name: E:\foo.pf J0000011: Job name: MBiek Direct Mail Test J0000020: Document 1 - Completed successfully  I'm trying to extract pieces from it using regex. In this case, I want to grab everything after Project Name up to the part where it says J0000011: (the 11 is going to be a different number every time). Here's the regex I've been playing with: Project name:\s+(.*)\s+J[0-9]{7}:  The problem is that it doesn't stop until it hits the J0000020: at the end. How do I make the regex stop at the first occurrence of J[0-9]{7}?


There are things that are seemingly OK but have problems within. For instance a food might seem OK but be poisonous. Or a translation might seem OK but in fact be awful since it has omitted or changed the main message. How can we describe such things? Even people might be seemingly nice but internally wicked!   I am particularly interested for words/phrases/idioms that describe the above-mentioned like translations.   For example:     This translations is the word I am looking for, it seems OK but   actually says something completely different to what the original   sentence says!   I am interested especially in a word with a formal register, which is suitable to be written in an academic text. Is outwardly good/flawless a good fit?

Is there an idiom or phrase for "what is apparent may not be the truth"  The use context is: You may see XYZ in zooming off in a Ferrari. But that is only because s/he works in the dealership as a mechanic.


I have a string:  java.lang.IllegalArgumentException: local part cannot be "null" when creating a Qname   which I'm pulling from a log file on a unix server.   and I have this same exact string which I'm pulling from a windows .txt file to compare against the string from the unix server:  java.lang.IllegalArgumentException: local part cannot be "null" when creating a Qname  I'm trying to determine if they are equal, but the .equals() method in java is letting me know that they are not equal.   How can I go about determining that they are indeed equal?

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I rolled a Hexblade Warlock for a campaign I am playing, with the Pact of the Blade and Cursebringer invocation.   What I did not account for is that because I am playing a Halfling, I have disadvantage with my weapon (a silver greatsword).  Is any way to remove disadvantage  due to being Small and wielding a Heavy weapon without multiclassing? If its only possible with multiclassing, what is the smallest number of levels required?  I was thinking about a spell that increases my size like the enlarge reduce, but that is a second level spell for sorcerers and wizard only.  I am looking for specific items/spells that a warlock could use to counter this disadvantage that i could use consistently, so not a potion or something.

A party member in a D&D 5e game I'm in is playing a halfling paladin. It occurred to me (for whatever reason) to ask what weapon they were wielding, and they said their main weapon was a maul, and their backup was a warhammer/shield combo).  Upon checking the , I discovered that  have the "Heavy" :     Heavy. Small creatures have disadvantage on attack rolls with heavy weapons. A heavy weapon’s size and bulk make it too large for a Small creature to use effectively.   The player seemed to be unaware of this (a similar character in Critical Role apparently wielded heavy weapons without issue - of course, CR is not necessarily a perfect demonstration of the rules as written).  As such, I was curious whether there is anything in the rules (i.e. not homebrew or a house rule) that cancels out this innate disadvantage for player characters, other than gaining advantage from some other source in combat.  (Note: the issue has already been resolved in our game between the player and DM, so it's purely a rules question.)


Is there a standard expression for  $$\sum_{r=0}^{n}\binom nr^2$$

I would like to prove inductively that $${2n\choose n}=\sum_{i=0}^n{n\choose i}^2.$$  I know a couple of non-inductive proofs, but I can't do it this way. The inductive step eludes me. I tried naively things like $${2n+2\choose n+1}={2n+2\over n+1}{2n+1\choose n}=2\cdot {2n+1\over n+1}{2n\choose n},$$  But I don't think it can lead me anywhere. I would like the proof to be as simple as possible.


I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I'm new to svn. I had to move svn repos from ec2 instance to another one. I wanted to reconstruct the svn from the exiting repos. I ran the command svn recover and got the recovery going. However, I cannot get a working copy out of these repos. When I ran sudo svnlook tree /home/svndir/repos/**** I could see the repository but I could not make a working copy out of these recovered repos. can anybody help me?

Recently our svn server was changed and we did a svn switch.  Since the working copy had a huge amount of unversioned resources, the working copy got locked and we started switching folder by folder for all folders under svn, which works perfectly fine.  But at the top most level of the repository, when I try to update files, I get the svn: Working copy '.' locked error and cleanup is not helping either. When I do cleanup, I get errors like these - svn: 'content' is not a working copy directory  Fresh checkout is NOT an option at all. Are there any other ways to cleanup and release the locks and do the switch completely ?  EDIT:  The last paragraph in JesperE's answer     If you get a "not a working copy" when   doing a recursive "svn cleanup" my   guess is that you have a directory   which should be a working copy (i.e.   the .svn directory at the toplevel   says so), but it is missing its own   .svn directory. In that case, you   could try to just remove/move that   directory and then do a local update   seems to be the solution to the problem in the repository. I have identified those folders and did a fresh checkout of those specific folders alone and wow, the locks are released in the subsequent cleanup! Thanks a lot JesperE !!  But, I still cannot figure out the svn switch error which now reads something like,     svn: The repository at   'svn://repourl/reponame/foldername'   has uuid 'm/reponame', but the WC   has 'b5b39681-0ff6-784b-ad26-2846b9ea8e7d'   Any ideas ?


Being a hobbyist coder and influenced by , I tend to organize the data I'm working with. Helping my little sister on her English made me curious about something.  Tenses in English is usually listed/grouped as    Simple   Past Simple Present Simple ...  Progressive/Continuous Perfect Perfect Progressive   or   Past   Past Simple Past Progressive ...  Present Future   You get the idea. They're either grouped by tenses or aspects. I like the latter, grouping them by tenses. So, one would get, for present tense   Present   Simple Progressive Perfect (Simple?) Perfect Progressive    Now, this grouping doesn't seem satisfactory. I'd group it as   Present   I   Simple Progressive  II (Perfect)   Simple Progressive     which makes a lot more sense to me. Though this grouping creates ambiguity, that is "I".   My question is what is the difference between "I" and "II"? What would one name "I", since "II" is the Perfect aspect. What exactly is "Perfect" and how it differs from "I"?    PS: I live in Turkey, so English isn't my native language. This categorization helps me internalize tenses better. Structured data is always easier to comprehend. I've seen a lot people (mostly classmates) struggle with Tenses, even after years of education. Discarding other possible reasons, this insufficient categorization is one of the reasons of the struggle, I think.  My reasoning in this grouping might be wrong. If so, you should ignore that. My question at its core would be 'If "II" is the Perfect aspect, which it is, what would be "I"? What should I name it?'  I'm fine with learning the right thing using the wrong method, as long as it works and makes sense to me. (You know, assuming my grouping is absurd.)

Non-native speakers often get confused about what the various tenses  and aspects mean in English. With input from some of the folk here I've put together a diagram that I hope will provide some clarity on the matter.  I offer it as the first answer to this question. Consider it a living document. Input is welcome, and good suggestions will be  incorporated into the diagram.    Nota bene: What this is not is a discussion of whether there are  more than two tenses in English. , to which this question is not intended to supply arguments one way or the other.  Here, the aim is to provide an overview of what constructions English-speaking people use for conveying information about actions referring to past, present, and future, and to provide it first and foremost to precisely the people who are likely to use "tense" as a catch-all term in their search, rather than to linguists who know better.  Breaking News There is now an excellent ELU blog article titled  . It is highly recommended reading.


I think all of the problems has been asked by me or others in the past. But my over all problem is that I am not able to combine all this solutions to the real picture I want to draw. Normally it is nice to seperate a complex problem into more simple ones and ask. But here I try to ask the complex question because I experienced that the solutions influence (in my case negativ) each other.    Description of the needs/prolems:   The left nodes (Phase) should be rotaed. I would prefere a solution with \rotatebox (node contents={\rotatebox{90}{#1}}}). The nodes (better would be rows) on the right are centered horizontal. Logical the picture have four rows and the nodes on the left and right need to display that. This means that one node (e.g. right of B) is centered vertical against its left node. Please see that PhaseC belongs to C1, C2 and long C3, so that the vertical alignment should represent that. () Connecting the nodes with arrow shouldn't be so hard I think. All have to be done relative. That means no cm, mm, pt or something like that. The number of nodes is not fixed. It could be that in row one are less nodes then in row four.   Some solutions:  \documentclass[tikz]{standalone} \usepackage{xltxtra} \usepackage{polyglossia} \setdefaultlanguage[spelling=new]{german} \usepackage{tikz} \usetikzlibrary{scopes,matrix,positioning,chains}  \begin{document} \begin{tikzpicture}     [         items/.style = {             draw,             align=center},         phase/.style = {             items,             fill=red!20,             node contents={\rotatebox{90}{#1}}}     ]     {[         start chain=P going below     ]         \node [on chain,phase=PhaseA];         {[             start branch=A going right,             every on chain/.append style=items,             every node/.style=on chain         ]             \node {One};             \node {Two};             \node {Three};             \node {Four};         }         \node [on chain,phase=PhaseB];         \node [on chain,phase=PhaseC];         \node [on chain,phase=PhaseD];         {[             start branch=D going right,             every on chain/.append style=items,             every node/.style=on chain         ]             \node {D1};             \node {D2};         }     }      % B     \node [right=of P-2,items] {right of B};      % C     \matrix (C) [         matrix of nodes,         row sep=5pt, %2\textheight doesn't work here, maybe a \nodeheight exists?         every node/.append style=items,         right=of P-3]     {         C1 \\         C2 \\         long C3\\     }; \end{tikzpicture} \end{document}   Produce this    Number 2 and 5 are not fullfilled. And I think number 6 would make problems in the future.

(Please feel free to offer a better and more precise subject title.)  I have two vertical chains with different count of nodes in it. But I want to visualize that some nodes of the right belong to one of the left. They need to appear in the same row/line. In the example code below you see Y and two nodes should appear on the right side of it.    The problem here is that I can not handle the right chain like it has 4 nodes and join them. Using \matrix make it impossible to use chain.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{matrix,positioning,chains,scopes}  \begin{document} \begin{tikzpicture}     [         myright/.style={             draw},         myleft/.style={             myright,             on chain,             fill=cyan!30}     ]     % LEFT     {[start chain=L going below,       every node/.append style=myleft]         \node {X};         \node {Y};         \node {Z};     }      % RIGHT     {[start chain=R going below]         \node [myright,right=of L-1] {belong to X};          \matrix [right=of L-2]         {             \node [myright] {belong to Y};\\             \node [myright] {also belong to Y};\\         };          \node [myright,right=of L-3] {belong to Z};     } \end{tikzpicture} \end{document}   btw: This question is related to .


I made some macros shown below, which outputs ordinary/partial derivative. I was checking whether they work as I expected, and found that \dif{y}{x} expands to \tfrac{\difd y}{\difd x} in align environment. I want to use \tfrac only in sentences, not in any display math modes. How should I change the definition in order to expands \dif{y}{x} to \dfrac{\difd y}{\difd x} in align environment, gather environment and so on?  I have another question. I think higher derivatives written with my command (especially partial ones) make a little much space before f. In terms of mathematical typography, which is proper: \frac{〈operator〉^{#1}#2}{〈operator〉#3^{#1}} or \frac{〈operator〉^{#1}\!#2}{〈operator〉#3^{#1}}?    EDIT (June 13, 2015 at 23:28 JST): The first question has been settled.  EDIT (June 15, 2015 at 14:21 JST): As David Carlisle points out, my question was a duplicate of  and commath package should not be used. Then, I have another question. In the linked page, there is a macro named \spx, the definition of which is in the below. Since we can see {^{#1}} in the definition, it seems to be an improved ^. What is the difference between this \spx and \^ and which should I use, "\(p)dif@nth and \@(p)dif" or "\spx without \@ifnextchar"?  My macros  % ----- differential operator ----- \def\difd@rm{\mathop{\mathrm{d}\!}\mathstrut} \def\difd@it{\mathop{d\!}\mathstrut} \def\makedifdrm{\let\difd=\difd@rm} \def\makedifdit{\let\difd=\difd@it} \makedifdit % default setting % % ----- ordinary derivative ----- \def\dif{\@ifnextchar[\dif@nth\@dif} \def\dif@nth[#1]#2#3{     \ifinner     \tfrac{\difd^{#1}#2}{\difd#3^{#1}}     \else     \dfrac{\difd^{#1}#2}{\difd#3^{#1}}     \fi } \def\@dif#1#2{     \ifinner     \tfrac{\difd#1}{\difd#2}     \else     \dfrac{\difd#1}{\difd#2}     \fi } % % ----- partial derivative ----- \def\pdif{\@ifnextchar[\pdif@nth\@pdif} \def\pdif@nth[#1]#2#3{     \ifinner     \tfrac{\partial^{#1}#2}{\partial#3^{#1}}     \else     \dfrac{\partial^{#1}#2}{\partial#3^{#1}}     \fi } \def\@pdif#1#2{     \ifinner     \tfrac{\partial#1}{\partial#2}     \else     \dfrac{\partial#1}{\partial#2}     \fi }   Definition of \spx and its usage  \newcommand{\spx}[1]{%     \if\relax\detokenize{#1}\relax         \expandafter\@gobble     \else         \expandafter\@firstofone     \fi     {^{#1}}% } \newcommand\pd[3][]{\frac{\partial\spx{#1}#2}{\partial#3\spx{#1}}}

The commath package use the TeX command \ifinner to select between inline math mode and display math mode. Because of this, it fail to work properly with some display math environments.  In the breqn package, we find:     The test \ifinner is unreliable for distinguishing whether we are in a displayed formula or an inline formula: (...) So we provide a more reliable test. But it might have been provided already by the amsmath package.   The more reliable test should be \if@display but only replace \ifinner with  \if@display in commath.sty not work. Any suggestion?


HP pavilion g6 with Intel® Core™ i5-3210M CPU @ 2.50GHz × 4  4gb ram,64bit

I have 14.04.5/16.04 or newer and an AMD GPU. I'm not getting the performance I want, and some programs say they need things like OpenCL.  I've heard about fglrx, but if I try to install it on my machine, it breaks and I have no GUI.  Is there anything I can do to get my AMD card working to its full potential?


In the equation $E_k=\frac12mv^2$ the fact that the kinetic energy of a moving object is not proportional to it's velocity seems counter-intuitive to me.  Put another way, it seems intuitive to me that if something with mass has an amount of kinetic energy when it's moving at a velocity, then if you doubled the velocity but kept the mass the same, then the energy would also double.   I'd really appreciate it if someone could supply an intuitive explanation.

As  says:     [...] the kinetic energy of a non-rotating object of mass $m$ traveling at a speed $v$ is $\frac{1}{2}mv^2$.   Why does this not increase linearly with speed? Why does it take so much more energy to go from $1\ \mathrm{m/s}$ to $2\ \mathrm{m/s}$ than it does to go from $0\ \mathrm{m/s}$ to $1\ \mathrm{m/s}$?  My intuition is wrong here, please help it out!


Suppose $f:\mathbb{R}^n\to\mathbb{R}^n$ is bijective and continuous. Is it possible that $f^{-1}$ is not continuous?  I can prove that for $n=1$ it is not possible, i.e. if $f:\mathbb{R} \to \mathbb{R}$ is bijective and continuous then $f^{-1}$ has to be continuous.  I also know that one can easily construct an example of a function $f : \mathbb{R}^2 \to S$, for some $S\subset\mathbb{R}^2,$ such that $f$ is bijective and continuous but $f^{-1}$ is not continuous. But this is different from what the above question is demanding.

Suppose we have a bijective continuous map $\mathbb{R}^n\to\mathbb{R}^n$ (relative to the standard topology). Must this map be a homeomorphism?  I have little doubt about this. I think that if it happens, I guess it's true, I've heard it is true, but I can not prove it.


"Java is pass-by-value" - However, there are things that confuses me. Please take a glimpse of my example  public class Main {      public static void main(String[] args) {          StringBuilder myBuilder = new StringBuilder("Michael");          editString(myBuilder);          System.out.println(myBuilder);      }      public static void editString(StringBuilder x){         x.append(" Ardan");     }  }   Output:  Michael Ardan   And this example:  public class Main {      public static void main(String[] args) {          int myInt = 10;          editInt(myInt);          System.out.println(myInt);      }      public static void editInt(int x){         x ++;     } }   Output:  10   I tried reading other articles and it all says that Java is always pass-by-value. I've done some test scenario. Comparing both example to each other made me think that Java's Objects are pass-by-reference and primitive types are pass-by-value. However, if you tried to replace the int primitive type into Integer Object, the result would be the same. I would love if somebody explain these two examples here.


How can I use mathematical induction to prove that $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ whenever $n$ is a nonnegative integer?

I'm trying to prove using induction that $9$ divides $n^3 + (n+1)^3 + (n+2)^3$ whenever $n$ is a non-negative integer. So far, I have:   Base case: $P(1) = (1) + (8) + (27) = 36, 36$ can be divided by $9$ so the base case is valid Inductive step: let $P(n)$ be the statement $9$ divides $n^3 + (n+1)^3 + (n+2)^3$. Assume $P(k)$ is true, so $9$ divides $k^3 + (k+1)^3 + (k+2)^3$.   And this is where I'm stuck. I'm not sure how to demonstrate that $9$ divides $P(n)$ when $n = k+1$. If someone could step me in the right direction that would be awesome. Thanks!


With , what is the most recent date which can be accurately determined, and why?   Is there an accepted time range, within which, accurate results can be attained using carbon-14 dating? I understand that the method can provide dating up to ca. 50,000 years into the past, but I'm interested in the other end of the time range: is there a point in time when younger (recent) specimens can no longer be dated with accepted accuracy?   I have read sources that place this limit anywhere between 50 and 500 years. I have read that this difficulty in the young-sample range is due to the fact that not enough material has been depleted to calculate accurately. I also understand the concerns with carbon-14 dating regarding the impact of fossil fuels / atomic activity in recent dating attempts. I also am aware of new carbon contamination when sampling.  I am a paintings conservator and have been requested to examine a panel painting from approximately 1550 A.D., and I have  evidence which supports this date. Would a carbon-14 analysis be of equal accuracy in this case?

For an example, when they tried to get the carbon dating for presence of Aboriginal people in Australia they get to the number 40,000. But it could be much earlier. Why is that 40,000 years limit for carbon dating methods?


I'm trying to add a checkbox to header of my table . For this purpose I've written the following lines of codes:   tableHead+=' <input type="checkbox" id="select_all"/> 	';  $("#select_all").click(function(){     alert('clicked!'); })   html

Results - Table
     <button id="download-json" class="btn" style="float:right;"> Get JSON</button>     <button id="download-csv" class="btn" style="float:right;"> Get CSV</button>

Execute a query first!

   Unfortunately, Altough checkbox appear on my table, when I clicked on it, nothing happens. I mean there is no alert message. What should I do to fix it?

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Between on and upon, which word better suits in the context of the following sentence.  The impression the victim made on / upon me when he testified was that of a witness of truth  I intend to impress a statement that the witness is a truthful witness.

Got boards tomorrow and I was going through some past years paper and one question stumped me. The leader counted _______ the cooperation of his colleagues. On/Upon both sound equally correct but I am not sure.  Could someone please tell me the correct answer and also explain when 'on' is used and when 'upon' is.


I have been receiving shocks from my washing machine.  My proximity voltage detector beeps near the chassis, drum and ground wire.  My voltage testing screwdriver also lights up when touched to them.  But when I test them with my multimeter I get no readings of any kind.  My multimeter has been tested and works well.  What is going on here? Thanks.

I live in Australia, with three-prong 240v power supply including ground prong. I own a simple plug adapter that does not include the ground connection. As far as I'm aware, using any appliance with this plug removes the safety of the ground protection, but should not have any further effects on the appliance. Instead, if I use this adapter with any of my appliances (washing machine, air compressor, etc) the chassis of the appliance becomes energised. By this I mean that I get a strong shock if I touch the chassis. Also, my proximity voltage detector and neon testing screwdriver light up when touching the chassis. My multimeter detects 0.3v running through the chassis (by the suggested method of touching one probe to the chassis and holding the other probe in my hand) Just touching both probes to chassis and trying all settings on multimeter gives infinite "1" result.  What is going on here? How serious is this problem?  Notes: 1. Yes, this is a follow-up to a previous question asked. 2. Yes, I have booked an electrician to come out, but it is always good to investigate yourself so that I can make sure that the electrician addresses the problem correctly. Also, I want to know if it's even safe for me to be in my house and use my appliances in the meantime.


I am using Ubuntu 18.04 and the default coreutils. I notice a particular behavior of the sort command which I am not sure how to explain.  Consider the following command:  $ cat <<EOF | sort 0- 01-                                     EOF 0- 01-   This output makes sense, because - has smaller ASCII value than 1 and thus this output is expected.  However, if I put one more character at the end:  $ cat <<EOF | sort 0-T 01-T EOF 01-T 0-T   This output doesn't make any sense to me as I think 0-T should come first. Why is this happening. What am I missing here? Am I having a wrong expectation?

I am trying to sort some simple pipe-delimited data. However, sort isn't actually sorting. It moves my header row to the bottom, but my two rows starting with 241 are being split by a row starting with 24.  cat sort_fail.csv column_a|column_b|column_c 241|212|20810378 24|121|2810172 241|213|20810376  sort sort_fail.csv 241|212|20810378 24|121|2810172 241|213|20810376 column_a|column_b|column_c   The column headers are being moved to the bottom of the file, so sort is clearly processing it. But, the actual values aren't being sorted like I'd expect.  In this case I worked around it with   sort sort_fail.csv --field-separator='|' -k1,1   But, I feel like that shouldn't be necessary. Why is sort not sorting?


How to reverse order the list containing strings where def view(self), because with reversed() I get an error that it can't be done with strings. Any help?   class Stack():      def __init__(self):         self.stack = []      def view(self):         for x in reversed(self.stack):             print(self.stack[x])      def push(self):         item = input("Please enter the item you wish to add to the stack: ")         self.stack.append(item)      def pop(self):         item = self.stack.pop(-1)         print("You just removed item: {0}".format(item))  stack = Stack()

So I can start from len(collection) and end in collection[0].  I also want to be able to access the loop index.


I know that Linear Discrimination Analysis (LDA) is used for classification and Multiple Linear Regression (MLR) is for regression. Lets say I have a matrix X (independent variables) and Y(dependent variables)  if the Y is continues and I make a regression , it becomes MLR if the Y is categories (like 1111122222) and I do MLR to make a relation , it becomes LDA?  can one explain it in simple words and illustrations ?

Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two classes?


My physics textbook says two electric field lines never intersect. Their explanation runs somewhat like this:     If two field lines crossed, there would be two different directions to the electric field at the intersection point, which is impossible by definition.   A similar explanation is provided as to why two stream lines never cross.   However, mathematically, two intersecting curves can have the same direction of tangent at their intersection point. For example, consider the $x-$axis and the curve $y=x^3$ is the $xy$ plane. Or any two curves of the form $y=x^{2k+1}$ with $k\in\mathbb N$, plotted for $-1<x<1$.  Is the explanation then wrong, considering these counterexamples? If not, why not? If yes, then what's the correct explanation?  Edit: The answers to  seem to focus on the very explanation I am having trouble understanding; I don't see how this is a duplicate of that one. I'd rather describe this as a follow-up question to that one.

The the title is self explanatory, I guess.  Why can two (or more) electric  never cross?


On Wordpress using the Astra theme I have archive pages containing titles and excerpts from 10 blog entries each, and when a new blog entry is written its title and excerpt go to the front. So the front archive page always has titles and excerpts from the 10 most recent blog entries, and the archive pages are arranged in reverse chronological order. This is pretty standard.  The problem is that the archive pages are not only ARRANGED in reverse chronological order: they are also NUMBERED in the same order. Thus the front page is labelled page 1, and the 10 entries posted BEFORE its 10 entries are on page 2. Correspondingly, “next page” refers to the next higher number. So for example the “next page” after page 7 contains excerpts from the 10 articles posted BEFORE the articles that are excerpted on that page.  I need the numbering to be the other way round.  For example if there are 117 entries than I want the page referring to the most recent entries (the 108th to the 117th) to be called page 12, and the previous page to that one (referring to the 98 the to 107th) to be called page 11.  This isn’t such a peculiar thing to do. It’s how issues of periodicals are numbered, for example.  How can I achieve this, whether by amending functions.php in the child theme (preferably), by writing a “Snippet” (next most preferred), or by amending archive.php in the Astra parent theme directly (least preferred, because of possible update problems)?  I know how to renumber the posts into direct chronological order, namely using the following PHP code. But unfortunately this DISPLAYS them in numerical order, which has now been reversed. So it causes the earliest posts to be excerpted on the front archive page rather than the latest ones!  <?php  add_filter(‘pre_get_posts’, ‘posts_by_forward_date’);  function posts_by_forward_date($query) { if(is_archive() || is_home()) { $query->set(‘order’, ‘ASC’); } } ?>   Any help will be much appreciated!

I have archive pages that each contain titles and excerpts from 10 blog entries. Both entries and archive pages are in reverse chronological order:   when a new blog entry is written its title and excerpt go to the top of the front page; when you are on one page and you click through to "Next page", you get the titles and excerpts for the 10 previous blog entries.   This is pretty standard for blogs.  But the archive pages are numbered by default in the same order. Thus Page 1 contains excerpts from the most recent 10 entries, Page 2 contains excerpts from the next 10 most recent, etc.  To be clear: at the moment, "Next page" refers to the page with the next higher number. Thus the front page, which contains excerpts from the most recent entry and the nine next most recent entries, is labelled Page 1, and the 10 entries posted before those 10 entries are on Page 2.  I need the page-numbering the other way round, namely in direct chronological order, so that for example if there are 97 entries then   entries 28-37 would be excerpted on Page 4, and the PREVIOUS page from there, containing excerpts from entries 18-27, would be called page 3.   How can I achieve this, whether by amending functions.php in the child theme (preferably), by writing a "Snippet" (next most preferred), or by amending archive.php in the Astra parent theme directly (least preferred, because of possible update problems)?  Edit  The following isn't a solution but it may be part of one. This re-numbers pages into direct chronological order, but unfortunately it also reverses the order in which they are shown (from reverse chronological to direct chronological). So it causes the front archive paget to contain excerpts from the earliest posts rather than the latest ones!  <?php  add_filter('pre_get_posts', 'posts_by_forward_date');  function posts_by_forward_date($query) {   if(is_archive() || is_home()) {     $query->set('order', 'ASC');   } } ?>


I wish to prove that $|\mathbb{R}-\mathbb{S}|=2^{\aleph_0}$ when $\mathbb{S}\subset \mathbb{R}$ is countable.  I want to say that $|\mathbb{R}-\mathbb{S}|= |\mathbb{R}|-|\mathbb{S}|$ but we haven't studied yet what subtraction of cardinals means (I can guess, though).  How could I prove this using only basic cardinal properties?

I'm currently reading a little deeper into the Axiom of Choice, and I'm pleasantly surprised to find it makes the arithmetic of infinite cardinals seem easy. With AC follows the Absorption Law of Cardinal Arithmetic, which states that for $\kappa$ and $\lambda$ cardinal numbers, the larger infinite and the smaller nonzero, then $\kappa+\lambda=\kappa\cdot\lambda=\max(\kappa,\lambda)$.  I was playing around with the equation $k+\aleph_0=\mathfrak{c}$ for some cardinal $k$. From the above, it follows that $\mathfrak{c}=k+\aleph_0=\max(k,\aleph_0)$, which implies $k=\mathfrak{c}$.  I'm curious, can we still show $k=\mathfrak{c}$ without the Axiom of Choice? Is it maybe possible to bound $\mathfrak{c}-\aleph_0$ above and below by $\mathfrak{c}$? But then I'm not quite sure such algebraic manipulations even mean anything, or work like that here. Certainly normal arithmetic does not! Thanks.


I got a GIS Data-set for swedish cities. The problem is that they have strange names such as:   TrÃ¤det  JÃ¤la  MjÃ¶nÃ¤s   Ã„lmhult  Did someone have the samoe problems? I think "Ã¶" for instance mean "ö" for example - but I am not sure if there is a system behind that.

I have a shapefile with names for Regions. These don't seem to contain special characters "Ä", "Ü", "Ö", "ß" but ugly hieroglyphs.  What can I do to display them correctly. If I import the shape as UTF-8 it doesn't work.  The names are in a dbase table. So is it possible to save a dbase table in UTF-8 or is there a different way of dealing with it?


I just thought of an interesting feature and was wondering if it is possible to do so in TeX or any of its derivatives. I'll explain it first.  Let's say we have the next simple LaTeX file. Imagine there is much more text.  \documentclass{article} \usepackage{graphicx}  \begin{document} Lorem ipsum dolor sit amet, consectetur adipiscing elit. In Figure \ref{fig:picture} you can see my picture. It's very interesting!  \begin{figure}[b] \includegraphics{my-picture} \label{fig:picture} \end{figure}  As you can see in the picture above, I like interesting pictures. \end{document}   Just a regular document. But what if, due to there being much more text, that last sentence is displayed above the image in the resulting PS/PDF file? The "above" wouldn't fit anymore. It should be below.  Is there any way to adapt the source text so that "above" fits? I was thinking of some kind of special \ref which adapts the text automatically, based on the final position of the image, relative to the text. For example,  As you can see in the picture \ref[adapt]{fig:picture}{above}{below}, I like interesting pictures.   If the final position of the referenced picture is above the \ref, it would say "above". If it is below the relevant text, it would say "below".  I already searched via Google but couldn't find anything about it. Does something like this exist? If not, is it easy to implement? I feel like it could be a nice package.

I would like to know if it is good practice, and if so how it can be achieved, to make references like: "as mentioned above...". Or am I going too far and should just type the word?  I've read something about varioref, but it seems to produce page or section numbers, but I can't find how you can just print if a section is above or below the reference.


i've tried to solve this following question without any success. can you help me with it please?  let $V=M_{2 \times 2}^\mathbb{R}$ and $f: V \times V \to \mathbb{R}$ so that $f(A,B)=tr(A^tMB)$ for every $A,B \in V$. when n=2, $V=M_{2 \times 2}^{\mathbb{R}}$ and $M=\begin{pmatrix}1&2\\ 3&5\end{pmatrix}$  find a representation of f as a sum of a symmetrical bilinear form and an anti-symmetrical bilinear form.  what i tried:  since from the details we can infer that in order for f to be symmetric, M must be equal to $M^t$ ($M=M^t$). now for a bilinear form to be symmetrical we need that $B(u,v)=B(v,u)$ for every $u,v \in V$, and for a bilinear form to be anti symmetrical it must follow $B(u,v)=-B(v,u)$. but i don't get to finding a representation of f as a sum of a symmetrical and anti symmetrical bilinear forms using the given values.  please help me if you can.   thank you very much.  (edit: this is not a theoritical question about proving that every biliear map can be written as a sum of biliner symmetric map and a bilinear anti-symmetric map. This question is about implementing the theory using the given details in order to obtain the needed representation. additionally, on that thread the answer is incomplete and not enough for me in order to solve this question. thank you very much).

Show that every bilinear map $\phi: E \times E \longrightarrow F$ can be written uniquely as a sum of a bilinear symmetric map ($f(u,v) = f(v,u)$, for all $u,v \in E$) and a bilinear anti-symmetric map ($f(u,v) = -f(v,u)$, for all $u,v \in E$).  My attempt:  I defined $$L_2(E,F) := \{ \phi: E \times E \longrightarrow F \ ; \ \phi \ is \ bilinear \},$$  $$W_1 := \{f \in L_2(E,F) \ ; \ f \ is \ a \ bilinear \ symmetric \ map \},$$ $$W_2 := \{g \in L_2(E,F) \ ; \ g \ is \ a \ bilinear \ anti-symmetric \ map \}$$  and I thought to proof that $L_2(E,F) = W_1 \ \oplus \ W_2$. I got to prove that $W_1 \ \bigcap \ W_2 = \{ 0 \}$, but I dind't get prove that $L_2(E,F) = W_1 + W_2$. How can I show this? I tried to prove by contradiction unsuccessfully.  Thanks in advance!


i'm trying to produce a few mockup pictures of a person using a tablet around the house. These are the conditions:   Camera Nikon D90, Lens 18-55 The pictures were taken in the morning Indoors but the room has a lot of natural light I didn't use zoom, the 'subject' was around half meter away from the camera Shooting Mode 'A', Image quality is RAW Fine, ISO 200 - 2000, F5.6v   The result was not good, the pictures have a lot of noise and grain.     How can i take crystal clear pictures without grain?  Thank you

What kinds of effects are present in digital images that are referred to as "noise"?    What are the different sources of noise?  What causes each type of noise? What are the characteristics of the different types of noise? How do the different types of noise visually manifest in the image? (i.e., do different kinds of noise "look different" is the resulting image, and how would they differ to the eye?) How can you minimize each type? What different post-processing techniques are most appropriate for each different kind?


Could someone help me to do this hard problem?I'd appreciate it!  Prove that if f(x) is continuous and one-to-one on the closed interval [a, b], then f(x) is stictly monotone on [a, b]. (Recall that strictly monotone on [a, b] means that either for all x and y such that x ∈ [a, b], y ∈ [a, b] and x < y, we have f(x) < f(y), or for all x and y such that x ∈ [a, b], y ∈ [a, b] and x < y, we have f(x) > f(y).)

Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone.   Attempt  Since we know that $f$ is one-to-one, for every $f(x)$ there is exactly one element $x_0$ that maps to it. Thus, if $f(x) = f(y)$, then $x=y$. Now let's suppose that $f$ isn't monotone. That is, it goes from nonincreasing to nondecreasing. Thus, on some interval $[a,b]$ we must have  $f'(x) < 0$ and on some other interval $[c,d]$ we must have $f'(x) > 0$. As a result we must have that $f'(x) = 0$ at some point. How do I show this contradicts the definition of $f$?


I want my text to be vertically middle in
 instead of align to the bottom.  My code:
    &nbsp;&nbsp;   Where Should I go ?
   And the result:    i have tried vertical-align:middle but it doesn't have any changes. Any other ways that it could make the text vertically align in middle?

I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers?

testing...


The problem is as follows:      Find the unique ordered triple of positive integers $(a,b,c)$ with   $a\leq b\leq c$ such that      $$\frac{1}{a}+\frac{1}{ab}+\frac{1}{abc}=\frac{25}{84}$$   The problem is easy to solve by first bounding $a$, then bounding $b$ and finally $c$. This is the solution I was given:  It's obvious that $a\geq 4$, otherwise $\frac{1}{ab}+\frac{1}{abc}$ would have to be negative, which we don't want. We also have  $$\frac{25}{84}=\frac{1}{a}+\frac{1}{ab}+\frac{1}{abc}\leq \frac{1}{a}+\frac{1}{a^2}+\frac{1}{a^3}=\frac{1+a+a^2}{a^3}$$  $$\frac{25}{84}\leq \frac{1+a+a^2}{a^3}$$  so $a\leq 4$ in order to satisfy the inequality, hence $a=4$. We can proceed in a similar manner to solve the rest of the problem.   Yes, this solution is simple and beautiful, but suppose I just want to solve this problem using a rigorous number-theoretic method (e.g. without inequalities). How would I go about doing this?  *EDIT* By the way, this problem was from part C of the 2013 COMC.

There is a unique triplet of positive integers $(a, b, c)$ such that $a ≤ b ≤ c$.  $$ \frac{25}{84} = \frac{1}{a} + \frac{1}{ab} + \frac{1}{abc} $$  Just having trouble with this Canadian Math Olympiad question. My thought process going into this, is:  Could we solve for $\frac{1}{a}$ in terms of the other variables? Then substitute that value in for each occurrence of $a$, to solve for $a$?  That's all I can really think of right now. It's a question I'm not exactly used to... It's sort of the first of these kinds that I've faced.  Thanks.


Please help me, I can't using bindValue() in PDOStatement.          $statement = self::$dbConn->prepare("SELECT  * FROM :tableDB WHERE id = :id");         $statement->bindValue(":id", $id, PDO::PARAM_INT);         $statement->bindValue(":tableDB", $tableDB, PDO::PARAM_STR);         $statement->execute();         $statement->setFetchMode(PDO::FETCH_ASSOC);         $result = $statement->fetchAll();   When i run this script.          $statement = self::$dbConn->prepare("SELECT  * FROM :tableDB WHERE id = :id");         $statement->bindValue(":id", $id, PDO::PARAM_INT); // Return true         $statement->bindValue(":tableDB", $tableDB, PDO::PARAM_STR); // Return true   But when run to:   $statement->execute(); // Return false.

Why can't I pass the table name to a prepared PDO statement?  $stmt = $dbh->prepare('SELECT * FROM :table WHERE 1'); if ($stmt->execute(array(':table' => 'users'))) {     var_dump($stmt->fetchAll()); }   Is there another safe way to insert a table name into a SQL query? With safe, I mean that I don't want to do  $sql = "SELECT * FROM $table WHERE 1"


Is the shell only an addon to the terminal, so that a terminal daemon has to work in order to to start a shell as its frontend. What controll does the terminal exherts upon the shell?

I think these terms almost refer to the same thing, when used loosely:   terminal shell tty console   What exactly does each of these terms refer to?


I have been repairing a water-damaged MacBook Air 2015. Initially the machine would only boot with the battery disconnected and power connected, but then die after around 20 minutes. The MagSafe light did not light up at all but still provided power to the computer.    I replaced the battery, which made no difference. I replaced the logic board which then allowed me to boot with the battery & power connected. The MagSafe still did not light up and the the computer would die after around 20 minutes.   I have just now replaced the I/O board. The MagSafe still does not light up and the battery does not charge, but the computer runs as normal with all apps open and full backlight etc.  I have reset the SMC and PRAM to no effect but I can't think what I could possibly replace at this point. The only remaining original part is the ribbon connector that links the I/O and Logic board but that looks in good condition. Does anyone have any suggestions at this point?  System report says that there is 0 mAh charge remaining in the battery  Battery: Yes  Charging: No   It also says that cycle count is 729 which it definitely isn't as it's a new battery.  Any help appreciated.

I'm far away from civilization thats why I need your help guys. My problem is: MacBook Pro 13" early 2015 is not turning on and charging and the trackpad is also dead.   Charger's LED does not shine by any light(red/orange/green) . But I tested my charger with another MacBook and charger is working. I tried to connect another charger. First 1-2 minute I can see green light and then LED turns off. Trackpad is not react to any action (like double click). Right now this is just some plastic area Turn off and turn on battery connector also didn't help me.   The laptop did not receive any damage and was not flooded with water. Day or two before I got it from safe and checked my email then closed it and put to the safe again(hotel standard safe) (everything was okay but I didn't remember battery charge percent at that day) then I open and figured out that MacBook is dead.


something selecting edges is very time consuming and you dont want to user the shoertcut to select everything just a small part connected by 2 edges.  how to accomplish that, meaning, I select an edge at one end and another at another end an automatically select everything between?  thanks

I have been using Blender for quite a long time and I just want to make sure that there isn't a better way of selecting edges, that I might not be aware of. It is so cumbersome to have to click every single edge when I don't want to select an entire edge loop but a portion of one instead. I was wondering if there is some way in to specify a start edge and an end edge and then be able to auto select every edge in between?


I kind of understand the meaning of conjugate to something but can't really get the clear picture of the concept. Some video lectures on youtube talk about it but they all seem to just say "Normal Distribution is conjugate to Normal" but for me to understand, it wasn't enough to get it. Hope to hear with least mathematical terms.

Someone told me that, Gaussian distribution is conjugate to distribution because a Gaussian times a Gaussian would still be Gaussian distribution ?  Why is that ? Say the following situation: $X\sim N(\mu_x,\sigma^2_{x})$ , $Y\sim N(\mu_y,\sigma^2_{y})$  Would a new variable, $Z=XY$ be normally distributed ??


I do not understand, why the air above the airfoil travels faster than the air below it? The air above has to travel faster than the air below so that both streams meet simultaneously at the trailing edge --- why do the streams have to meet simultaneously ?   PS : I understand the Bernoulli principle and how the lift is created by the pressure difference and all that.

I understand the common explanation of lift, which describes the airflow over the top of the wing as moving faster than the air below the wing.  However, I don't quite understand why the air moves faster.  I've read some explanations citing a circulation effect among others, but haven't found a good, clear explanation for the exact cause.  Can someone help me out?


I am kind of new to javascript and trying to understand some non trivial - at least so i hope :) things.  my question is general, but i have a specific example which can help me ask my question and help you understand what i mean.  the example:  function updateBookmark(bookmark){     var index = _.findIndex($scope.bookmarks, function(b){         return b.id == bookmark.id;     });     return index; }   obviously the findIndex function is declared somewhere (in our case - lodash.js)  and it gets two parameters (at least two visible parameters: a data set, and a function)  first question:  in this example, what is b? how does b gets its value? i understand b is each of the data set's objects, but i mean - what is going behind the scenes here so b will be what it is??  second question:  the author chose to pass an anonymous function which equals b.id with bookmark.id,  i understand that he can use bookmark.id where he is using it, but how does findIndex has access to this bookmark?!   this function as i concluded earlier is declared somewhere else, does it get all the variables in the scope some how? what is going on here?  Thanks in advance to responders and sorry for the messy question... Jim.

How would you explain JavaScript closures to someone with a knowledge of the concepts they consist of (for example functions, variables and the like), but does not understand closures themselves?  I have seen  given on Wikipedia, but unfortunately it did not help.


Find all positive integers n such that $n + 3$ divides $n^2 + 27$.   I am quite stuck on how to conclusively show all of the solutions. I tried look at the intersections of $y = n^2 + 27$ and $f = x(n + 3)$ where is $x$ is some number. But it still involves setting $x$ values. Any help would be much appreciated.

Let the sum of all integers $n$ such that $(2n^2+9/n+3)$ is an integer be $A$, what is $|A|$?  I tried expressing it to:  $k$ is an integer, $(n+3)k + 0 = 2n^2 + 9$, $n(2n-k) + 3(3-k) = 0$, from which I couldn't move on,  I also tried $(n+3)k + 0 = 2n^2 + 9$, $k = 2n$, $2n^2 - 2n^2  + 9 - 6n$. $9-6n/n+3$ is an integer, $9 - 6n = 3(3-n)$ though now I also do not know how to move on.


I am fairly new to both Blender and Python. I am running the latest version of Blender to date (2.9.1), shipped with Python (3.7.7) I am trying to install/import some Python modules that facilitate audio processing. These modules : PyAudio and SoundDevice I managed to figure out how to install several of these modules using the terminal commands on my Mac, and they seem to have installed successfully. However, these modules seem to ONLY be installing to my system Python (3.9). As instructed, I have tried changing the terminal directory by going into the Python terminal inside blender, printing the sys.exec_prefix, and copying it into terminal before install:    >>> import sys    >>> sys.exec_prefix    '/Applications/Blender.app/Contents/Resources/2.90/python'   But it seems that the new modules just go into my system Python(3.9) and I can't seem to get anything added into Blender's Python(3.7). Am I missing something?  Are there any comprehensive posts or tutorials about how to add modules specifically to blender's python?  Any help would be appreciated.  (I'd prefer advice and resources specific to Mac as PC directory structures and terminal prompts seem to be different). Thank you.

I'm currently developing a script for Blender to handle Mesh Frequency Decomposition.  The script is nearly complete, but i need one more thing: The SciPy library to compute eigenvalues and eigenvectors.  Following the installation instructions on , I'm able to install it as well as Numpy. Numpy works fine, but I can't even import SciPy:  Traceback (most recent call last): File "/CAF_FD.py", line 4, in <module> ImportError: No module named 'scipy' Error: Python script fail, look in the console for now...   By the way, I'm working on Linux 64 bit and I've installed SciPy and Numpy with my package manager.  Edit: When I try to use SciPy with a terminal prompt, it works.


Given:  MariaDB on CentOS 7  Table telephones   tp_id //primary key  tp_p_id // foreign key to programs table tp_num_type //fax, primary, hunt, cell, alarm tp_num // the telephone number   Table programs (our term for different locations) 1:many with Telephones   p_id //primary key p_name // program name   Question I'd like to have a query that selects the program data and then tp_num as tp_primary where tp_num_type = 'primary', and then also tp_num as tp_fax where tp_num_type = 'fax'.  What I have...  SELECT p_name, tp_num as tp_primary  FROM programs  INNER JOIN telephones ON p_id = tp_p_id WHERE p_id = 1 AND tp_num_type = 'Primary';   I just don't have any idea how to do the second inner join from tp_num as tp_fax. Can anyone point me in the right direction? Or do I have to do a subquery for this?  Thanks,

I have 2 tables. One (domains) has domain ids, and domain names (dom_id, dom_url).  the other contains actual data, 2 of which columns require a TO and FROM domain names. So I have 2 columns rev_dom_from and rev_dom_for, both of which store the domain name id, from the domains table.  Simple.  Now I need to actually display both domain names on the webpage. I know how to display one or the other, via the LEFT JOIN domains ON reviews.rev_dom_for = domains.dom_url query, and then you echo out the dom_url, which would echo out the domain name in the rev_dom_for column.  But how would I make it echo out the 2nd domain name, in the dom_rev_from column?


Suppose that $G$ is a group s.t. $x^2=1$ for all $x \in G$. Prove that $G$ is abelian.    If we assume that $x^2 = 1$ for all $ x \in G$, and suppose that $a,b \in G$ and if $x=ab$ we see that $x^2 = abab =aabb = a^2 b^2$. Simplifying we see that $ab=ba$, and because we know that $x= ab$, we see that $1=1$. Therefore it is abelian. $\square$  Is this sound? I'm struggling with this stuff because I think it's so simple and I'm concerned I'm overthinking it.  I'd like to contest the mods decision that this is an exact duplicate. Though there are similar questions, as has been linked, it is not the same thing. If it is a problem with the abstract algebra tag, then delete it and allow it to be an active thread under other tags.

Let $G$ be a group, and suppose that $a= {a^{-1}}$ for every $a\in G$. Prove that $G$ is Abelian.    I know that I need to prove that ${a^{-1}}$ = a and use right multiplication. I also know that I need to declare a, b $\in$ G and go from there, but I'm confused when I get to   (${a^{-1}}$${b^{-1}}$) = ab.


I use blenrig 5..   when I skinning I realize that the bone isn't in correct position, i need to fix my bone position without affecting any weighted mesh (skinned mesh)

I have a skeleton rig and mesh configured in blender that I have imported from 3rd party application.  The rig and mesh are already working together correctly in blender.  I would like to adjust the position of some of the bones to align with animations from another 3rd party application.   Currently 1 or 2 bones cause the mesh to deform incorrectly due to differences in bone position between the animations and the armature for my skeletal mesh.  So the question, is it possible to move the position of the bone without the attached mesh being deformed during the move and maintain the existing weight painting for the new bone position?  So for example in my rig the neck bone is positioned more towards the back of the neck surface, but the neck bone in the animation is more centered, so when I apply the animation the head of my mesh is artificially leaning forward due to relocation of neck bone.  When I try to move any bone in my rig the attached mesh moves with it  Hopefully the makes some form of sense :oo  Thanks in advance


The police arrested a man. The police have arrested a man.  I don't know the difference between these two sentences. Could someone please explain?

I have never had this problem before. But after seeing some questions posted on ELU, I started to doubt. I have been through links1, pages of grammar books2, a lot of questions3 posted here and ELU. I now still can't seem to understand how the past perfect is exactly used. The references sometimes even contradict each other.  What I had understood so far was      The past perfect is not necessary if we are not 'going back' to the earlier past, and simply moving from one event to another.   but I then saw a lot of other 'rules' including      If the sequence is clear, the past perfect is not needed.   which is slightly different, less 'narrow' and can be applied in more situations than the first ruleA, and      The past perfect is optional only when talking about an action at a specific time.   This is confusing. Can anyone here clarify things out please?    A For example, for  Doing the survey [completed] -> Showing the result      We showed the result of the survey we did.      If the second rule is applied, the sentence above is fine (the sequence is clear), but not if the first rule since we are not moving from any event to the next and possibly even going back.    1  and   2 Practical English Usage (2005) by Michael Swan, Collins Cobuild Student's Grammar (1991). Upper-Intermediate Cutting Edge.  3 including , , ,  etc.


I'm trying to create a module in JavaScript. I want my module to have something like a class. I'm not sure if what I"m trying is possible. Essentially, I want to be able to do this in JavaScript:  var myObject = new myCompany.myLibrary.myClass(); myObject.myFunction();   Currently, I'm trying the following:  var myCompany = myCompany || {}; myCompany.myLibrary = (function() {         var myProperty = null;      var anotherProperty = 'Hello';      return {         myClass: function () {           return {             myFunction : function() {               console.log(anotherProperty);             }           };         }     }; })();   When I do this, I get an error that says "undefined is not a function". Is it possible to do what I'm trying to accomplish in JavaScript? If so, what am I doing wrong?

I'm not that into dynamic programming languages but I've written my fair share of JavaScript code. I never really got my head around this prototype-based programming, does any one know how this works? var obj = new Object(); obj.prototype.test = function() { alert('Hello?'); }; var obj2 = new obj(); obj2.test();  I remember a lot discussion I had with people a while back (I'm not exactly sure what I'm doing) but as I understand it, there's no concept of a class. It's just an object, and instances of those objects are clones of the original, right? But what is the exact purpose of this ".prototype" property in JavaScript? How does it relate to instantiating objects? Update: correct way var obj = new Object(); // not a functional object obj.prototype.test = function() { alert('Hello?'); }; // this is wrong!  function MyObject() {} // a first class functional object MyObject.prototype.test = function() { alert('OK'); } // OK  Also these  really helped a lot.


I have diamond helmet/chest piece/legs with protection 2 or 3 on each one. I'm wondering if there's any point to wearing all at the same time or would I be better off just wearing one piece with the highest enchant and the rest regular, unenchanted, diamond?

Prior to 1.4.6 it was a well known fact that the protection enchantment on armor was strictly superior to the other enchantments and that simply having a few pieces with protection III/IV would max out this protection, leading to the best possible set of armor.  Now that this has , however, I'm curious to see if anyone has analysed what the optimal armor configurations now are?  Presumably it will be some combination of protection enchantments and other enchantments, going by the description of how enchantments work now on the wiki.  Or, are we forced to choose one or more types of protection to max out?  (This would be the case if there are not enough total enchantments possible to max out all areas).  If this is the case, it would be great to see some analysis of how to optimise that choice as well.  I've looked around but haven't found any good mathcrafting on this question yet.  Furthermore, beyond protection against taking damage, can someone include some explanation of the hidden utility bonuses?  For instance, Blast Protection has been described in wiki sources as reducing the knockback effects from explosions, and Fire Protection is described as reducing burn time.  Do these effects scale and max out at some enchantment level, and does Projectile Protection similarly reduce the knockback effect from projectiles?


In US, when people work together, they may look for a colleague or any person to tell something or for any other reason, asking other collegues/people such a question:      Have you seen Michael?    or      Did you see Michael?    Which is considered right if the question refers to an activity (in our case "see") during a day and not the past in general?

What is the difference between     Did you watch this movie?    and     Have you watched this movie?


Why doesn't this command output "1"?  echo 1 | echo   I imagine it working this way:  1. echo 1 (outputs 1) 2. | echo (takes the 1 as an input, then echos it)   Isn't this what should happen?

I have a file named my_file.txt whose content is just the string Hello. How could I redirect its content to the command echo?  I know I have the commands less, cat, more... but I need to do it with echo.  I tried this:   $ cat my_file.txt | echo   and also this:  $ echo < my_file.txt   But in both cases it appears only a blank in the stdout, not the content of my_file.txt.  How could I do that?


I work as a java dev so I know java and I'm learning python. Is this enough for developing ubuntu desktop apps or I need more? I would like to focus on good gui builders and I know kava swing is pretty poor.

I want to create an Ubuntu desktop app, specifically to replace Gwibber.  I can code in Java, Python and a few other technologies. Adobe Flex would have been an option until Adobe decided to suck some more and stopped support for AIR on Linux.  Note - I don't care about supporting other OS's. It will be a personal Ubuntu specific app. It can I open-source, I don't mind extra help.  It should integrate seamlessly with Ubuntu, notifications and all.  I guess Python it is, is that correct? How do I get started?


When I run sudo apt update I get the following error: Hit:1 http://in.archive.ubuntu.com/ubuntu focal InRelease Hit:2 http://in.archive.ubuntu.com/ubuntu focal-updates InRelease                Hit:3 http://in.archive.ubuntu.com/ubuntu focal-backports InRelease              Hit:4 http://dl.google.com/linux/chrome/deb stable InRelease                        Hit:5 http://in.archive.ubuntu.com/ubuntu focal-security InRelease                  Hit:6 http://in.archive.ubuntu.com/ubuntu focal-proposed InRelease                  Hit:7 http://ppa.launchpad.net/kivy-team/kivy-daily/ubuntu focal InRelease          Hit:8 http://ppa.launchpad.net/kivy-team/kivy/ubuntu focal InRelease Ign:9 http://ppa.launchpad.net/webupd8team/java/ubuntu focal InRelease Err:10 http://ppa.launchpad.net/webupd8team/java/ubuntu focal Release   404  Not Found [IP: 2001:67c:1560:8008::15 80] Reading package lists... Done E: The repository 'http://ppa.launchpad.net/webupd8team/java/ubuntu focal Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.  How to fix this and update !!!

When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do?


How do I derive the formula for curvature through differentiation?  $$ k(t)= \dfrac{(x'y''-x''y')}{(x'^2+y'^2)^\frac32} $$  I know that $k(t)=$ the modulus of $ T'(s) $ where $T$ is the unit tangent vector

How do you derive the formula for unsigned curvature of a curve $\gamma (t) = (x(t), y(t)$ which is not necessarily parameterised by arc-length.   The formula given is $$|\kappa (t)| = \left|\frac{x'' y' - y'' x'}{((x')^2 + (y')^2)^{3/2}}\right|$$  All the definitions of curvature in my notes give it in terms for an arc-length parameterisation $T'(s) = \kappa(s) N(s)$. This is apparently meant to be 'easily derivable', am I missing something?


I am centering inner div insTabsContainer using margin: 0 auto but it's not getting center. Will you guys tell me what's I did wrong here.  HTML    .insTabsContainer {   margin: 0 auto; }  .insTabs {   position: relative;   float: left;   width: 32%;   height: 25px;   background-color: #E5E7E9;   text-align: center;   line-height: 20px;   text-transform: uppercase;    font-size: 13px;   color: #2C3E50;   border-radius: 6px;   margin-right: 5px;   cursor: pointer; }

Text

Text

Text

How can I horizontally center a
 within another
 using CSS?

Foo foo


And I know there's std::cin, but that requires the user to enter a string, then press ENTER.  Is there a way to simply get the next key that is pushed without needing to press ENTER to confirm

I can never remember how I do this because it comes up so infrequently for me. But in C or C++, what is the best way to read a character from standard input without waiting for a newline (press enter).  Also ideally it wouldn't echo the input character to the screen. I just want to capture keystrokes with out effecting the console screen.


I’ve recently noticed that some questions are marked as “highly active“ while actually they are not. This is a recent  of a question that never hit the “Hot Network” list and its total views are, after 3 days, just about 80. Below the “locked” banner there is another banner which says: “Highly active question. You have enough reputation to answer or unprotect this question.” Which is the same banner used for  real “highly  active questions“!!! Have conditions for being classified as “highly active questions” changed recently?

Questions can be protected (i.e. marked "highly active").   What does it mean for a question to be protected? Why are some questions protected? Who can protect and unprotect questions? Who can answer a protected question? How are protected questions displayed? When should I protect or unprotect a question? When does the Community user protect a question?


Is there any way to create many objects at once in Python?   Let say, that I want to populate a list with 1.000.000 object instances. Instead of initializing objects one-by-one in loop, is there any way to create them in one call?  Iterating one-by-one takes some time and I am looking for a way other than running many threads to reduce this time.  My adventure with Python started a month ago, so I am quite unaware of many Python specific tricks. Any hints how to deal with this problem?

Code like this often happens: l = [] while foo:     # baz     l.append(bar)     # qux  This is really slow if you're about to append thousands of elements to your list, as the list will have to be constantly resized to fit the new elements. In Java, you can create an ArrayList with an initial capacity. If you have some idea how big your list will be, this will be a lot more efficient. I understand that code like this can often be refactored into a list comprehension. If the for/while loop is very complicated, though, this is unfeasible. Is there an equivalent for us Python programmers?


I bought this hp mini off an old friend. well it has been running for quiet a while and it seems like since 2001 (that'as the recent modified dates seen on the files). This is my first laptop with Ubuntu and it seems I've made a mess with the system since then. I was just wondering if I could erase and start over with a fresh copy since is no such option to restore to factory command similar to Windows. I recently upgraded it, even-though I had no idea what I was doing and it changed from 10.04 to 12.04. But the power cord came out, and battery died while I was asleep. Regardless, I should say that the upgrade went half. Nevertheless, I logged-in finally, but now all kinds of errors pops-up as I have duplicate things going on. All I wanted is to start from scratch with fresh install. How can I achieve this??

I would like to see a full how-to guide on how to install Ubuntu.


Here is the product of cycles. My textbook goes right to left multiplication. $$(1,4,5)(7,8)(2,5,7)$$  An observation here is that I don't think these cycles are disjoint and therefore they are not commutative. So far I have only done calculations with disjoint cycles so I wasn't sure how to handle this.   I calculated the permutation to be after writing the cycles out in table notation.  $$\sigma =  \begin{pmatrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8\\ 4 & 1 & 3 & 5 & 8 & 6 & 2 & 7 \end{pmatrix} $$  However, if I inverse the process and split $\sigma$ into cycles, I get  $$(1,4,5,8,7,2)$$  Is it because I am not multiplying product of disjoint cycles that I am not able to inverse the equation? Am I just doing this completely wrong?

I am trying to learn how to find the product of non-disjoint cycles, as you may have guessed from the title. I have the basic idea, but I do not understand it entirely.  I am trying to find $(1352)(256)$ and $(1634)(1352)$, multiplying from right to left.  Please give me some hints/suggestions.  Thank you.


I need to allow several clients to affect the volume of a central server.  Can I change the audio master volume via command line in Ubuntu 12.04?

How to increase or decrease overall system volume from terminal like I was doing it in the GUI?


"Children are continuously forced to hear stereotypes about themselves because of their gender, but what if a child wanted to challenge their fate?"  I know it doesn't begin with a question word, but I was still curious if it could pass as a question.

Is this sentence a question or a statement (or other). It ends with a question, so I used a question mark. (Just ignore the tech jargon.)     I get that this should show me the PID of the SIGTERMing process and I successfully   compiled it, but how do I use it?   Edit: Another question, should it be written as (which is correct and which is clearer?)     I get that this should show me the PID of the SIGTERMing process and successfully   compiled it, but how do I use it?


I have a CSV file in which some fields contain values greater than 255 characters. I want to ask that wether joining the CSV file with a shapefile overcomes the 255 character limitation of shapefile and displays the data in CSV completely. If not, then what is the solution for it?

The maximum text string for a field in a geodatabase is 320 characters.    The data I am importing has long character strings and it seems to be truncating when I convert into shapefile at the max text string and messing the fields up.  Is there a way to extend this to 700-1000 characters?


I'm pretty sure we need to prove via contradiction, but in the past I've only ever had to prove that there exists at most a set number of roots.

Assume that $f: \mathbb{R} \rightarrow \mathbb{R}$  is differentiable.  If there exists an $L<1$ such that for each $x \in \mathbb{R}$, $f'(x)<L$, prove that there exists a unique point $x$ such that $f(x)=x$.  So far I have that where I fixed $a$ to be zero and came up with three cases to show existence for  $f(0) = 0$, $f(0) < 0$, and $f(0) > 0$  $f(0)=0$ was fairly trivial following from the mean value theorem but the other two cases I was only able to eliminate half of the possible fixed points by contradiction and I need help showing it explicitly.  Edit as to avoid confusion here is the work I have garnished so far:  From the mean value theorem it follows for some arbitrary $a,b \in \mathbb{R}$ and $a\neq b$ that there exists a point $c$ such that $a<c<b$ or $b<c<a$ then implies that $\frac{f(b)-f(a)}{b-a}=f'(c)$ and this is because it is differentiable on $\mathbb{R}$ and, by convention, is also continuous on $\mathbb{R}$ as well.  Then the result of $\dfrac{f(b)-f(a)}{b-a}=f'(c)$ then follows for $L<1$ such that $\forall x \in \mathbb{R}$ means $f'(x)<1$ from our hypothesis. Which then follows  (*) $\dfrac{f(b)-f(a)}{b-a}=f'(c)<L<1 \Rightarrow f(b)-f(a)<L(b-a)<b-a$  Now without loss of generality choose $a=0$ and let $b$ be some arbitrary value in $\mathbb{R}$ then there are three cases that need to be considered for the value of $f(a)$:  (i) $f(0) = 0$, (ii) $f(0) < 0$, (iii) $f(0) > 0$  (i) For $f(0)=0$   Then $0$ is a fixed point of point of $f(x)$ and it follows from (*) that if $f(0)=a=0$ then $f(b)-f(0)=f(b)<Lb<b$ which shows that $f(b)<b$ thus shows that for any arbitrary value $b\in \mathbb{R}$ that no $f(b)=b$ thus shows that $0$ is the only fixed point if $f(0)=0$  (ii) For $f(0)<0$  Suppose there exists a fixed point $d>0$ then:  $\frac{f(d)-f(0)}{d}<L<1 \Rightarrow d-f(0)< dL<d \Rightarrow -f(0)<d(L-1)<0\Rightarrow 0<-d(L-1)<f(0)$ but this contradicts that $f(0)<0$  thus no other fixed point exists if $d>0$ when $f(0)<0$  (iii) For $f(0)>0$


I need to find every single file that has executable permissions in my system, i think they end with x@.  I tried to ls every file and then grepping the output to match files with x@.  Like this:  ls -l | grep x@   But that just lists for the current directory and:  ls -ld | grep x@    Did not show all files. I need to search in all subdirectories. And I'm using FreeBSD tools (OS X).

I have got the directory called Test and a few directories inside it. Both Test and the directories inside it have executable files. I'd like to print them with ls. I'd use this command.  ls -l `find Test/ -perm /u=x,g=x,o=x -type f`   Is this a good/right/quick command or not?  My solution is:  find Test/ -executable -type f -exec ls -l {} \;   and got the same result as warl0ck and pradeepchhetri offered.


Let $R$ be a finite ring with $1\neq 0$. Suppose there are $x,y\in R$ such that $xy=1$. I have to prove that this implies $yx=1$.   I have read the question  but I dont understand why $xy=1$ implies that left multiplication with $y$ is one to one. Could you explain? Thanks.

Let $R$ be a finite ring with identity $1$, and assume $\exists x,y\in R$ such that $ xy=1$. How can I show it implies $yx=1$?


I am trying to delete a particular string from the linked list, but i keep getting null pointer exception error! Any help fellas?  public void delete(String deleteName) {          LinkedListNode current = head;         if(head==null){             System.out.println("Nothing to delete from the list! Insert data.");         }         // for head         else if(current.getName()==deleteName){             head=current.getNext();         }         // for tail         else if(findTail().getName() == deleteName){             while(current.getNext().getNext()!=null ){                 current = current.getNext();             }             current.setNext(null);         }         else{             while(current.getNext().getName()!=deleteName){                 current=current.getNext();             }             current.setNext(current.getNext().getNext());         }         System.out.println("");         System.out.println(deleteName +" has been deleted from the list.");      }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I'm trying to securely keep a user logged in using php but am worried about security.  So I've been going by this . But There's still a few things I don't quite understand.  Please keep in mind I'm not an expert by any means, so please speak as if you were talking to a child.  function onLogin($db, $user) {   $token = GenerateRandomToken($db); // generate a token, should be 128 - 256 bit   storeTokenForUser($db, $user, $token);   $cookie = $user . ':' . $token;   $mac = hash_hmac('sha256', $cookie, 'SECRET_KEY');   $cookie .= ':' . $mac;   setcookie('rememberme', $cookie, time() + (86400 * 7)); }   My question is, how is this secure? I will be storing it in a cookie, which under my knowledge is viewable by users. The "SECRET_KEY" in hash_hmac must have something to do with it but I didn't find much information on how to use it in the manual.  Will the "SECRET_KEY" in hash_hmac be the way that I can secure my cookies? If so, how do I use it? Will it be the same everytime? or should I generate a random ID for it?  Thanks for your time. Greatly appreciated.

I want my website to have a checkbox that users can click so that they will not have to log in each time they visit my website. I know I will need to store a cookie on their computer to implement this, but what should be contained in that cookie?    Also, are there common mistakes to watch out for to keep this cookie from presenting a security vulnerability, which could be avoided while still giving the 'remember me' functionality?


When using tags in spoilers, the tags appear through the spoilers, for example:      This is a spoiler, here is a .   Which, if you look carefully, also makes the tag text visible.  Which, kinda invalidates the point of the spoilers...

Tags in spoilers are always visible, even if you don't put your mouse on the spoiler (on  for example). See the screenshot:      Looks a bit strange on this site too:        that needs !


I am from Gujarat,India.at restaurants in my city,they provide raw sliced onion as condiment.it tastes really sweet and not at all pungent. How can I remove pungency from onion?I tried soaking them in cold water but they become wet and I just want them dry.

How can I tone down the intensity of raw onion? Some onions have a more acute taste and smell than others of the same type, and I would like to avoid them in salad dish, or making dips with raw onion. If effectively none, an alternative solution that can also be helpful is to find out what condiments can I add/mix with raw onion to cancel out the intensity of the the acute taste.  [EDIT] There is a uniquely (IMHO) sweet taste to onion that I like. But accompany with that is the acute scene and flavor to it that I wanted to get ride of. I do not want to waste away the taste of onion, but remove the acuteness and remain the sweetness.


$$I=\sum_{k=1}^{98}\int_{k}^{k+1}\dfrac{k+1}{x(x+1)}dx$$, then which of the following are correct?  A) $I<\dfrac{49}{50}$  B) $I>\dfrac{49}{50}$  C) $I<\log_{e}99$  D) $I>\log_{e}99$  My attempt is as follows:-  $$I=\sum_{k=1}^{98}(k+1)\int_{k}^{k+1}\dfrac{1}{x}-\dfrac{1}{x+1}dx$$ $$I=\sum_{k=1}^{98}(k+1)\left(\ln\left|\dfrac{k+1}{k+2}\right|-\ln\left|\dfrac{k}{k+1}\right|\right)$$  $$I=\left(2\ln\left|\dfrac{2}{3}\right|-2\ln\left|\dfrac{1}{2}\right|\right)+\left(3\ln\left|\dfrac{3}{4}\right|-3\ln\left|\dfrac{2}{3}\right|\right)\cdots\cdots+\left(99\ln\left|\dfrac{99}{100}\right|-99\ln\left|\dfrac{98}{99}\right|\right)$$  This is looking like a telescopic terms but middle terms are not cutting entirely.  $$I=\left(-2\ln\left|\dfrac{1}{2}\right|+99\ln\left|\dfrac{99}{100}\right|\right)-\left(\ln\left|\dfrac{2}{3}\right|+\ln\left|\dfrac{3}{4}\right|+\ln\left|\dfrac{4}{5}\right|\cdots\cdots+\ln\left|\dfrac{98}{99}\right|\right)$$  $$I=\left(2\ln2+99\ln\left|\dfrac{99}{100}\right|\right)+\ln\left|\dfrac{99}{2}\right|$$  $$I=\ln2+99\ln99-99\ln100+\ln99$$ $$I=\ln2+100\ln99-99\ln100$$ $$I=\ln\left(\dfrac{2\cdot 99^{100}}{100^{99}}\right)$$ $$I=\ln\left(198\cdot\left(\dfrac{99}{100}\right)^{99}\right)$$  So is $198\cdot\left(\dfrac{99}{100}\right)^{99}>99$?  Is $\left(\dfrac{99}{100}\right)^{99}>\dfrac{1}{2}$, any way to find this if its true without finding the actual value.  Actual answers are $B,D$. Am I missing some trick here?


I need some guidelines as to where to start, what to learn (everything I need to learn to do the job of web design). I'm having quite a bit of free time at my current job and I've finished with codecademy's HTML & CSS course. What should I learn next? I would prefer something I could learn at my workplace, but that would mean no YouTube videos (can't plug in headphones and can't install software as I'm using the company's PC). I need as many suggestions as I can possibly get as I really want to learn this properly.

I'm very interested in learning web development and have learned some basics regarding HTML and CSS a few years back from W3Schools, but I never learned how to develop websites that are up to today's standards, i.e. free-flowing sites without the use of tables to govern the design of the site.  What are some good resources that I can start with?


If I use a GLM with the identity link, is there any difference to a linear model? For example, if I use a Gamma GLM with identity link and an Inverse Gaussian GLM with identity link, what is the difference from these to a linear model? I've tried it in R and they give different coefficients, so I presume the models are different, but I don't see how.

My question relates mostly around the practical differences between General Linear Modeling (GLM) and Generalized Linear Modelling (GZLM). In my case it would be a few continuous variables as covariates and a few factors in an ANCOVA, versus GZLM. I want to examine the main effects of each variable, as well as one three-way interaction that I will outline in the model.  I can see this hypothesis being tested in an ANCOVA, or using GZLM. To some extent I understand the math processes and reasoning behind running a General Linear Model like an ANCOVA, and I somewhat understand that GZLMs allow for a link function connecting the linear model and the dependent variable (ok, I lied, maybe I don't really understand the math). What I really don't understand are the practical differences or reasons for running one analysis and not the other when the probability distribution used in the GZLM is normal (i.e., identity link function?). I get very different results when I run one over the other. Could I run either? My data is somewhat non-normal, but works to some extent both in the ANCOVA and the GZLM. In both cases my hypothesis is supported, but in the GZLM the p value is "better". My thought was that an ANCOVA is a linear model with a normally distributed dependent variable using an identity link function, which is exactly what I can input in a GZLM, but these are still different. Please shed some light on these questions for me, if you can!  Based on the first answer I have the additional question: If they are identical except for the significance test that it utilized (i.e., F test vs. Wald Chi Square), which would be most appropriate to use? ANCOVA is the "go-to method", but I am unsure why the F test would be preferable. Can someone shed some light on this question for me?