I was going to change Facebook's default login button with my custom image like .  I mean like this:    But  which state its against Facebook's policies.  Is it really a violation? If it is how come Mashable using custom image? Can someone answer me?  Update  This is the exact image I would like to use.    Facebook mentioned like this in .     While you may scale the size to suit your needs, you may not modify   the “f” logo in any other way (such as by changing the design or   color). If you are unable to use the correct colour due to technical   limitations, you may revert to black and white.   So my sign in with Facebook image violating Facebook policy in anyway?

I would say most websites with a somewhat thought-through graphical design use social media icons (i.e Twitter, Facebook, YouTube, etc) which are altered to fit the theme and design of the site.  Now, my boss insist we only use the ones provided by say Facebook or Twitter themselves (in fear of getting sued or lose credibility), but sometimes it just doesn't look very good on the site.   What is the common practice for these things? What do you risk by using an altered logo? What should I tell my boss?  I'll provide a few examples, what'd happen if I put any of these on a site?


There are 2 objects  1)   var obj1 = { id: 1, firstName: 'someFirst', lastName: 'someLast', status: 'active', }   2)   var obj2 = { firstName: 'test', status: 'disable', }    how can I change the key value of the first object based on the key values of the second object? Expected result is:   obj1 = { id: 1, firstName: 'test', lastName: 'someLast', status: 'disable', }   Many thanks!

I need to be able to merge two (very simple) JavaScript objects at runtime.  For example I'd like to:  var obj1 = { food: 'pizza', car: 'ford' } var obj2 = { animal: 'dog' }  obj1.merge(obj2);  //obj1 now has three properties: food, car, and animal   Does anyone have a script for this or know of a built in way to do this?  I do not need recursion, and I do not need to merge functions, just methods on flat objects.


Suppose I pick (using a single choice) an element $q_1$ from a nonempty set $U$. I then pick $q_2$ from the set $U/\{q_1\}$, $q_3$ from the set $U/\{q_1, q_2\}$ and so on. At each stage, the set in question is guaranteed to be non-empty. Thus, I have constructed a sequence $(q_n)_{n\in\mathbb{N}}$ using a single choice each time. Thus, I can safely assume that no (countably infinite) axiom of choice was used in the construction of this sequence, right?

Let $S$ be an arbitrary infinite set. As a part of our homework, I have the following question: Question: How can I construct an injection $\mathbb{N} \to S$? Intuitively, I understand that such an injection should exist but describing it explicitly is probably not possible. Therefore, I think we need to use the Axiom of Choice: If $X$ is a set of non-empty sets, then there exists a choice function $F$ on $X$, i.e. a function on $X$ such that for all $M \in X$, we have $F(M) \in M$. Our class was given the following hint: Construct a family of $A_n \subseteq S$ with $|A_n| = 2^n$ for all $n \in \mathbb{N}$. Next, construct a family $B_n \subseteq S$ of non-empty and pairwise disjoint subsets. However, I do not really know what to do with this hint. Maybe the condition $|A_n| = 2^n$ indicates that we should use the power set of some set with $n$ elements but that is just a vague idea. I would really appreciate it if you could help me advancing with this problem.


I would like to split a long string (as in the example below) when this string is in a variable:  \documentclass[a4paper]{article} \def\parametre{0azertyuiopqsdfghjklmwxcvbn1azertyuiopqsdfghjklmwxcvbn2azertyuiopqsdfghjklmwxcvbn3azertyuiopqsdfghjklmwxcvbn} \usepackage{seqsplit}  \begin{document}  \begin{minipage}{10cm} \seqsplit{\parametre} %not correct \end{minipage}  \begin{minipage}{10cm} \seqsplit{0azertyuiopqsdfghjklmwxcvbn1azertyuiopqsdfghjklmwxcvbn2azertyuiopqsdfghjklmwxcvbn3azertyuiopqsdfghjklmwxcvbn} %correct \end{minipage}  \end{document}


Is it possible to get the class calling a function in JavaScript?  For example:  function Foo(){ this.alertCaller = alertCaller; } function Bar(){ this.alertCaller = alertCaller; }  function alertCaller(){     alert(*calling object*); }   When calling the Foo().alertCaller() i want to output the class Foo() and when calling Bar().alertCaller() I want to outbut Bar(). Is there any way I can do this?

function main() {    Hello(); }  function Hello() {   // How do you find out the caller function is 'main'? }   Is there a way to find out the call stack?


My goal is to find the general form for the asymptotic cardinality of a compound arithmetic progression.  I'm not affiliated with a university and I certainly don't have any obligation to continue my research.  However, it is very fulfilling to me.  I spend my time in the library; I study through the books on the shelves and I don't really have anyone to tell me that my efforts are not good enough.  The problem comes in when I realized that if I was stronger in Analytic Number Theory, then I could start to look for the general estimate for the asymptotic cardinality of any compound arithmetic progression, and I'm terribly curious about how it works out.  I am jealous of professional students with academic affiliations, access to reviewers, and journals; terribly.  I admit that and it's a big obstacle.  And I'm envious that they had the opportunity to enjoy more prestigious settings.  I wish I could get a foot hold like that too.  But at the same time I just don't think it's going to be possible for me to be published or be respected on the same level, no matter what I do.    Is it healthy for me to behave like this?  Or am I being too optimistic in thinking that I have something to contribute that could blossom into graduate level, age appropriate research and/or a funded project?  The point is that I've given up looking for a degree or trying to participate in the research projects of others; it places the burden on them to find a place for me in their work and I'd rather be sharpening my own offering instead of going on a wild goose chase.  Math doesn't require the same kind of budgetary overhead, or anywhere near the same level of oversight as the life sciences.  I don't need a lab.  I don't need dangerous chemicals or expensive equipment, and I don't need a workshop, either.  The other question (of which this was marked as a duplicate) was asked by a much more established individual that already finished a Master's degree and wanted to collaborate on somebody else's research; putting together a CV to apply for a research spot is much easier when there's something to anchor it.

I graduated with a Masters of Engineering, concentrating in digital signal processing, in particular medical and audio, almost two years ago. I've always been interested in research, but due to personal circumstances I could never commit a lot of time to working on a research project with a professor, and obviously didn't get a chance to publish anything. Now that I'm more settled and have much more time on my hands, I started getting involved in some open source projects and reading some technical literature (engineering, mathematics) that I couldn't get to before. However, I'd still like to find someone to to collaborate with on a research project who is already established in the field and publishes papers. Part of the reason I want to do that is to be able to eventually apply for a Ph.D. program in a good school, and having publications would be a great thing on my resume.  What I'm trying to find out is how I can work on a research project similar to those graduate students work on as a part of their studies if I'm not a student anymore? Should I contact my old professors from the university? Is it possible to find some "open research" team that accepts collaborators from outside? Do I have to do it on my own (quite frankly I'm not sure I can give myself a good enough quick-start)? In short, I'm willing to volunteer my time in exchange for a possibility of publication in the future. Can I do it, and if yes then how?


Render preview looks like this   But when I hit render, I get this image   Does anyone know why? I'm using filmic blender color management if that makes a difference.

This is meant to solve this problem once and for all. What is every reason an object isn't showing up in a render or viewport in when using the cycles render engine?


ArgumentError raises when passing plain text to "order_by". I'ts occurs with version 0.9.8, but not with version < 0.9.8 or > 0.9.8.  q = session.query(Person) q.order_by('RAND()') >> ArgumentError: Textual SQL expression 'RAND()' should be explicitly declared as text('RAND()')   questions: 1. Is there any official documentation about it? 2. With new versions, is this a good practice to pass plain text, or it is better to wrap it with text()? 3. Is this error raises with more functions other then order_by?

How do I select one or more random rows from a table using SQLAlchemy?


I have a red stop sign in my toolbar; it reads as follows:          An error has occurred. Run package manager from the right click menu or apt-get in a terminal to see what is wrong. The error message was:     "error. brokencount > 0 this usually means you have unmet dependencies."      I tried to solve the problem with:   sudo apt-get install -f   I got this message:  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following extra packages will be installed: libmysqlclient18 The following packages will be upgraded: libmysqlclient18 1 upgraded, 0 newly installed, 0 to remove and 572 not upgraded. 3 not fully installed or removed. Need to get 0 B/2.892 B of archives. After this operation, 3.471 kB disk space will be freed. Do you want to continue? [Y/n] y dpkg: error processing archive /var/cache/apt/archives/libmysqlclient18_10.1.18+maria-1~trusty_amd64.deb (--unpack): libmysqlclient18:amd64 10.1.18+maria-1~trusty (Multi-Arch: no) is not co-installable with libmysqlclient18 which has multiple installed instances E: Sub-process /usr/bin/dpkg returned an error code (1)

I'm running ubuntu 14.04. I cannot use software center to install anything, even a local deb package so I have to rely on Terminal.  Recently I was trying to install mysql-server which generated error which I could pin-point was the required version of libstdc++6 . My system had 4.8.x while mysql 5.6 required >=4.9. Trying the usual upgrading process and unsuccessful, I consulted my sys admin, who tried installing the 4.9 package manually(using a local .deb package), which failed as well citing unmet dependencies.   At present, what I have is a system with error saying no new software can be installed.  The sudo apt-get install -f gives following output:  Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... failed. The following packages have unmet dependencies:  libstdc++6 : Depends: gcc-4.9-base (= 4.9.2-10) but 4.9.1-0ubuntu1 is installed  libstdc++6:i386 : Depends: gcc-4.9-base:i386 (= 4.9.2-10) but 4.9.1-0ubuntu1 is installed E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.   I checked for held packages using  dpkg -l | grep ^h dpkg -l | grep hold   Result: nothing.  Also tried to find the broken package, if any but the file  /var/log/dist-upgrade/apt.log doesn't exist.  So, what should/can I do now.


The case is quite typical. I’ve to compare two (multi-)polygons layers of administrative regions, with l2 being lower level (let’s say municipalities – 2811 records) than l1 (let’s say provinces – 785 records). Both layers are stored in a PostGIS DB. Each municipality refers the corresponding province through a foreign key. Municipality’s boundaries should fit to the Province’s boundaries but, due the digitizing errors, it’s not case and we have the following situation with overlaps and gaps, as shown below  The aim is to adjust boundary of each “municipality” features (l2) to match to the shared part of boundary of its corresponding province (l1). I would like to male all treatments in PostGIS I tried various treatments:   testing with various tolerance  SELECT a.cod_mun, st_snap(a.geom, b.geom, tolerance) AS st_snap  FROM municipality a, province b  WHERE mun_cod_prov = cod_prov But the results it not good at all (with tolerance 50)   Extract each intersected parts  I easily extracted small parts of municipalities (in blue here below) that correspond to the intersection of municipality in the undesired provinces but didn't find yet the solution to group the relevant zonez and retrieve the whole municipality with matched borders SELECT row_number() OVER (ORDER BY a.cod_mun) AS gid, st_difference(a.geom, b.geom) AS geom FROM (     SELECT mun_cod_prov, st_multi(st_union(a.geom))::geometry(MultiPolygon,25830) AS geom     FROM municipality     GROUP BY mun_cod_prov     ) a,     province b WHERE b.mun_cod_prov =cod_prov    Buffer  My third option was to create a buffer surrounding the municipalise and then clip through st_intersects the output geometries to the corresponding province. This worked but got me another unsolved problem in the others borders. I guess I¡ve to clip with the neighbouring communities  So I’m wondering if is there an efficient way to achieve this spatial treatment in PostGIS or if someone treated a similar case Configuration: PostgreSQL 10.7 Postgis 2.4 I read similar posts at  and  but did not find how to adapt either.

Here's the problem:   Where:  1: department boundary  3: polygons inside department boundary that "touch" the department boundary(1). They are not necessary fitting well inside  2: holes between 1 and 3  I need to "adjust" polygon shapes (3) to "match" department boundary (1) filling the holes (2)    Using PostGIS:  My 1st approach was to get the st_pointonsurface of all numbers 2 and number 3 by departments. Then assign the holes (2) to the nearest polygon by pointonsurfaces between each other.  See image (from another department boundary but same problem, exceeding dotted lines with no fillcolor are polygons zones that exceeded department boundary that I've already cut off by department boundary so no problem there)    This worked but got me another problem::   some (lots of) holes (2) that where attached to the nearest polygon (by st_pointonsurface) were really long lines     Here (2) are the holes that were attached to the nearest polygon, and the result is 'strange' new polygons with really long lines.    I can use any of ArcGIS 10, Quantum GIS and PostGIS to solve this, but I can't get a way to solve this.    EDIT  How about using topology? what rules may be useful for this problem?    How topology will resolve when multiple polygons are fighting to get the same hole?    EDIT 2  Using geometry approach with PostGIS.  one idea: - make buffers of the multiple polygons that are inside the department boundary - get the st_intersection between buffered polygon vs original polygon + hole. This way the new "buffered" polygon only keep the buffer where the "hole"-intersected-area is touched.   This may work with simple examples .. but with real world holes and polygons.. This will leave us another problem: the overlaps between different buffered polygons inside hole areas..


I'd like to use the PWM I/O on the SAMA5D2 Series Microprocessor (Microchip).What I'm confused about is why each PWM channel has a high and low output pin. The datasheet specifies     Each channel controls two complementary square output waveforms.   My understanding is that you only need one of these outputs to drive an external peripheral such as a fan. In what instance would two complementary PWM outputs be used?  Also, do I need these two complementary waveforms to drive a 4-wire PWM fan?  I've added a I/O description and timing diagram example from the datasheet for clarity.

PWM channels in certain microcontrollers such as the SAM3X8E have two complementary square output waveforms, PWMH and PWML, per channel. What is the purpose of having two waves that are the inverses of each other?


There is a probabilistic method to solve it. But I am not familiar with probability. I am trying to compute it by analytic method, such as using L Hospital's rule or Stolz formula, but they are not working.

I'm supposed to calculate: $$\lim_{n\to\infty} e^{-n} \sum_{k=0}^{n} \frac{n^k}{k!}$$ By using WolframAlpha, I might guess that the limit is $\frac{1}{2}$, which is a pretty interesting and nice result. I wonder in which ways we may approach it.


I have point data of population density that I have plotted to show density with proportional circle symbols. This is straightforward with many ways of achieving this in different software and packages. But I would also like to use colours to show not only density by proportional symbol but also have the proportional symbols coloured to represent different values from another map layer, a raster map.  So for example, I want the largest symbol size to be coloured red, orange or yellow depending on the value of the spatially corresponding raster cell. So each symbol size will have different colours depending on the raster.  Is there an existing R function that does this (I cannot find one)? Or is there a way of clipping the (coloured) raster map by a point map that is displayed with proportional circles?

I'm back again with more R mapping questions! This one is concerning symbolizing points by a certain attribute with graduated/proportional circles.   DATA: My full code can be found  if you're interested. My CSV of interest is . Ethiopia shapefile   I've plotted points from the CSV over a shapefile. For the sake of brevity, here's the heavily abridged version of my code:   library(raster) library(rgdal)  #set your working directory  #read in eth shapefile eth <- readOGR(dsn = "D:/Mapping-R/Ethiopia", layer = "ETH_adm0")  #read in total branch location csv branches <- read.csv("Branches_Africa.csv", header = TRUE)  #transform branches data frame to spdf for mapping coordinates(branches) <- ~Lon + Lat  #plot shapefile with point overlay plot(eth) points(branches$Lon, branches$Lat, col = "blue", pch = 16, cex = .5)   As you can see in the branches CSV, there are several different attributes. In my case, I would like to symbolize the "share" attribute with graduated/proportional circles, as seen here:   Ideally I would also like to change the colors of each point as well to match the QGIS symbology as closely as possible.   If you look at my full code, you'll notice that I've not used ggplot to map, so I would prefer the solution not come from that package (or would ggplot make things easier once I've transformed all the data to fit the package?).  I tried using spplot as per  post with:  spplot(branches, "share", col.regions = brewer.pal(9, "Reds"), cuts = 8, scales = list(draw = T))   but the code gave me the following error: Error in fill.call.groups(args.xyplot, z = z, edge.col = edge.col, colorkey = colorkey,  : number of colors smaller than number of factor levels  I also tried to work with mapCircles from the rCarto package, but I had no luck there either.  SO, how can I change the symbology of branches$share so that graduated/proportional (and preferably differently colored) circles are displayed instead of just one size/color?


Where can I download Ubuntu 18.04 Beta 1 ? Is it the daily build from today ?

I'd love to test the latest Ubuntu alpha/beta (otherwise known as "Ubuntu+1"), but I can't find it.   Where can I find download for the pre-releases of Ubuntu?


Can anyone tell me what depository I'm missing? If I search for say "Apache" at apps.ubuntu.com it comes up with what I'm looking for, if I search for it in the Software center all it comes up with are books and maybe some games.  Right now it looks like it's using the following sources:    Thank you, David

Some applications don't pop up in the search even when you type in their name. Take for instance Sushi. When you type in "sushi" into the search box, it fails to throw up the application. Only when you type in "gnome-sushi" does it appear. This is despite the fact that the application has "sushi" by itself in the application description. There are other applications which don't spring to mind right now, but I've discovered before.


Many of us know Euler’s famous identity:     $e^{i\pi} + 1 = 0$.   But if we add -1 (subtract 1) to both sides we get:      $e^{i\pi} = -1$   then natural log of both sides and:      $i\pi = \ln(-1)$   Next we multiply both sides by 2:     $2i\pi = 2\ln(-1)$   Which by basic logarithm rules is equal to:     $2i\pi = \ln({-1}^2) = \ln(1) = 0$   so     $2i\pi = 0$   which can’t be true as either 2, i or $\pi$ would have to equal 0. My best guess is that logarithms just plainly aren’t defined for negative values, I just assumed this was just true logarithms bounded under the real numbers, though I might be wrong. If someone could help it would be great.  Thanks.

I was playing around with Euler's identity   $$\begin{align}e^{i\pi}&=-1\\\\\frac{\log{(-1)}}{i}&=\pi\\\\\frac{x \log(-1)}{i}&=\pi x \end{align}$$   And when I had $x=2$  $$\frac{\log(1)}{i}=2\pi$$Which is equivalent to $$\frac{0}{i}=2\pi$$  How can this be?


I am trying to solve this problem, the answer should be 15/20 = 75%.  However, I am not sure how this was calculated and want to understand the underlying concept.  A program core consists of five conditional branches. The program core will be executed thousands of times. Below are the outcomes of each branch for one execution of the program core (T = taken, N = Not taken).   Branch 1: T-T  Branch 2: N-N-N  Branch 3: T-N-T-N-T  Branch 4: T-T-T-N  Branch 5: T-T-N-T-T-T   This behavior remains the same. For dynamic schemes, assume each branch has its own prediction buffer and each buffer initialized to the same state before execution.   What is the prediction accuracy for the 2-bit predictor, initialized to weakly predict taken? (Answer is at the beginning but I'd like to understand the concept of the calculation.)


i have some scripts that take as input one or multiple paths as on argument.  The script is run like that: myScript.py D:\Folder1,E:\OtherData\Files  In the script, i split the path arguments in the comma and i read the paths.  The problem is that Python adds a \r in the end of each path for no reason. So the script tries to read D:\Folder1\r and E:\OtherData\Files\r.  Why is this and how can i solve it?

What is the Python equivalent of Perl's chomp function, which removes the last character of a string if it is a newline?


I had Oreos and milk a while ago and left my half-full cup of milk out on the counter. Afterwards I noticed that the crumbs had surfaced in a circular coin-sized glob, and just now I looked again to see all of the crumbs seem to have compressed into a more dense glob at the very center of the cup.   Why does this happen?

Why does a cork ball float to the side of a glass as illustrated in the following GIF? What is the physical phenomenon behind this observation and why does it happen?


While working on websites that involve WooCommerce I keep on having random GET value generated on the address bar. For example, I recently added an E-Commerce using WooCommerce plugin to this site, . When we used to open the site before having WooCommerce, the site URL displays at it is  . Now, it adds this random get value ?v=ae41a6d38b78 to the site address. How can I remove the random get value that is added to the address?  I have looked everywhere but I wasn't able to find solutions to it, instead I kept on running into the same kind of sites that display the GET value.

I'm new to wordpress, I set up everything, but there's something that bothers me: on every single URL or link, there's a "?v=hash" appended everywhere (example.com/?v=d21feabed96b).  I tried to see inspect every plugin, I don't understand how this parameter is added.  It looks like it's added in js, because if I see the source, there's no trace of this hash, but I can see in firebug live source.  Plugins installed:   jetpack sumome wp-piwik wp super cache woocommerce   Theme: Storefront  I tried to disable everything, but still I get this hash, does anyone knows how and why it's added?  I'm also using cloudflare


Please consider the following EntityFieldQuery. I would like to add a conditional parameter depending on the user's permissions. I'd expect the query would combine these statements and return both visibilities. However it ends in an empty result set. (Removing one of the statements gives the expected result).  $query = new EntityFieldQuery(); ... if(user_access('access public')) {   $query->propertyCondition( 'visibility', 'public' ); } if(user_access('access private')) {   $query->propertyCondition( 'visibility', 'private' ); } ...   So how could I make both conditions apply without blocking each other?

I have never had the need to do this before today, but it doesn't seem like you can make OR queries with EntityFieldQuery, since db_or is used for select queries.  An example would get to all entities that has a date field where the value is null or after today.  Am I missing something or some trick or is this simply not supported?


Prove that an integer $n$ is divisible by $3$ if and only the sum of it's digits is divisible by $3$. This how I proceeded  $n=\overline{a_1a_2...a_k}$ Now we get  $$n=a_1\cdot10^k+a_2\cdot10^{(k-1)}+....+a_k$$ Then I find no clue.

I'm trying to teach myself some number theory. In my textbook, this proof is given:  Example (2.3.1) Show that an integer is divisible by 3 if and only if the sum of its digits is a multiple of 3. Let $n=a_0a_1\ldots a_k$ be the decimal representation of an integer $n$. Thus $n=a_k+a_{k-1}10+a_{k-2}10^2+\cdots+a_010^k$ where $0\le a_i<10$ The key observation is that $10\equiv1\pmod3$, i.e., $[10]=[1]$. Hence $[10^i]=[10]^i=[1]$, i.e., $10^i\equiv1\pmod 3$. The assertion is an immediate consequence of this congruence.  I don't understand the last statement. Why does it follow from that congruence?


I am requested some explanations on some topic in professional email exchanges, and I don't know if I can end the mail with : "Please do not hesitate to contact me for further information". Actually I am French and I use here a kind of translated expression often used in French. I would like to know if it sounds good enough for a professional email in English, or is there a better way to express this idea that I am ready to provide more explanations if it is needed.

How to ask "If you have any problem then ask me" in polite manner.  While discussing problem with my brother in chat, he most of the times ask me how you get to the solution and then I have to explain each step. And in between he keep on asking me questions. This was about chat so there is no problem.   Now if I'm writing a mail, what I do is I write the solution to the problem and ask him that 'if you have any problem then ask me'.   He is my brother so he understands but if I do same with with any professor then that will be a trouble for me.   Please help me with some phrases which means "if you have any problem then ask me" but in polite manner.


The spell "Frost Fingers" from page 318 of the module "Icewind Dale: Rime of the Frostmaiden" says:  The cold freezes nonmagical liquids in the area that aren't being worn or carried.  This wording makes it a bit unclear, whether creatures are then stuck in the frozen water, because surrounding water could count as "worn or carried". How is this spell to rule especially underwater with swimming creatures who are in the area of the spell (15 ft cone, originating from the caster)? Are they then restrained or possibly enclosed in ice?

What defines a worn or carried object, for the purposes of spells like Burning Hands and Firebolt? They ignite items, but specifically not things worn or carried.  Does carried mean wielded in hand, such as a staff? And does Worn pertain to only clothing and armor?  For instance, if a Wizard gets hit by Firebolt, would his component pouch and spellbook that are just on his person be ignited?


how can I make my animated robot pick up an object (a pole) without making two separate animated key signatures one for the robot and one for the object?

I'm doing a simple robot arm that turns the arms around and do different movements. But I can't figure out how I should do if the robot should pick up something like a small box?  Should the box be connected in some way to the armature to be able to follow the  movements of the arms? Perhaps I want the robot to pick up the box after some time and not from the beginning, how do I connect it then or what is the best approach?


Let $A\subset\mathbb R^n$ be a closed and convex. A points $x\in A$ is said to be an extreme point if it cannot be represented as a nontrivial convex combination of points in $A$. Let $\operatorname{ext}A$ denote the set of extreme points of $A$. I've stumbled upon the observation that "$A$ contains lines if and only if it has no extreme points" (page 37, remark 1, in Hug and Weil (2010), pdf can be found ). I can see that if $A$ contains a line $L$, then it cannot have extreme points. Indeed, given any $x\notin L$, then the (closed) convex closure of $\{x\}\cup L$ must equal everything between $L$ and the line parallel to $L$ intersecting $x$, and such set has no extreme points. Geometrically, this amounts to the following construction: $\qquad\qquad\qquad$ However, I'm not sure how to proceed for the other direction. How do I prove that if $A$ contains no lines, then there must be at least an extreme point (or equivalently, that the absence of extreme points implies that at least one line is contained in $A$)?

I am wondering how to prove the following theorem: Let $S \subset \mathbf{R}^{n}$ be a non-empty closed convex set. Then $S$ has at least one extreme point iff $S$ does not contain any line. Extreme point $x \in S$ means that there is no couple of points $y, z \in S$ and $\lambda \in (0;1)$ such that $x = \lambda y + (1-\lambda)z$. I know that every non-empty closed convex set can be represented as an intersection of all closed half-spaces containing the set but I do not know if it is helpful in proving the theorem.


I was wondering if you could simultaneously load 2 mods such as a hacked client like Nodus, and TMI? I have tried to just place both jar files but that did not work.

I have found a few mods for minecraft I like a lot. I know you cant use them all at the same time. I know that some go together well, so how do I find out what goes with what?  Is there a way to load some for now, and unload them later so that I can change them out? I got a patch device but I don't think it works that well.  I tried to play with this stuff on my own but I got things so messed up that I had to delete everything and start over. So what am I doing wrong?  KH


I am trying to create my first model in Blender using  (you can see the files of the model ). In the  (04:25), when one vertex is pulled down, only some of the vertices of the ring-shaped structure are pulled down.  However, when I try to do the same, the entire ring goes down (see ).   How can I make sure that when I pull down one of the vertices, only the adjacent vertices (not the entire ring-shaped structure) is moved down (like shown in the video)? I am using the following Blender version: version: 2.83.2, branch: master, commit date: 2020-07-09 05:50, hash: 239fbf7d936f, type: Release build date: 2020-07-09, 04:24:13 platform: Windows

I'm facing this frustrating "feature" that I can't seem to remedy; when I duplicate an object (and now, even when I create two completely new objects), their transformations/scaling is synchronized. This is extremely annoying when trying to use any sort of transformation keyboard shortcut.  It should be noted by going to the properties menu (N) and manually setting the properties works just fine.  For instance, here is just the camera selected (trust me, I made sure):   And when I try to transform by clicking+dragging on the X axis OR by hitting G->X, this happens:   They are not grouped (verified by going to the Groups list up in the Scene panel) and they do not have parents (verified by going to Object->Relations).  I have tried the unlink command as well, to no avail.  I have seriously run out of options; what did I change to have my G->X shortcuts transform multiple objects? It seems completely at random, too; certain objects seemed to be "linked" to other random objects, and this "linking" is guaranteed when duplicating even when I do a non-linking duplicate (Shift+D).  What gives?


Why do we limit the definition of a function to only one y per x?  For example, the square root function.  We only allow the principal square root of a number, rather than, say, the square root of 9 being both 3 AND -3.  Why is this?  Thanks!

I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe


I get raw milk and to somehow pasteurize it, I boil it. The milk strongly curdled showing that it is spoiled and rotten (definitely, not suitable for drinking). Is it totally bad milk and I should throw it away? or it still can be used for making yogurt and cheese?

I have a large quantity of raw milk at my disposal, and am trying to find creative ways to use it.  Various web sites (, , and many others) have suggested that raw milk, even (perhaps even especially) after it begins to sour, can be used to make yogurt.  I've also  for yogurt cultures to grow.  Which is it?  Please note this question is specifically about , not spoiled milk, which is not edible. And please assume that the sour raw milk being used is free from harmful bacteria and pathogens and is safe to consume.  I'm not asking about food safety here, I'm asking: Is it possible to make yogurt from sour raw milk?


How to use a definite integral to find the following limit: $\lim\limits_{n\to\infty}\left(\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{n+n}\right)$  Which is equal to $\ln(2)$. I know that there are a lot of series which converge with radius of convergence 1, so I'm assuming i'd have to use this fact in order to integrate the series, but I have no idea what to do here. If someone could drop a hint that would be great

Prove that : $\displaystyle \lim_{n\to \infty} \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{2n}=\ln 2$    the only thing I could think of is that it can be written like this :  $$ \lim_{n\to \infty} \sum_{k=1}^n \frac{1}{k+n} =\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{1}{\frac{k}{n}+1}=\int_0^1 \frac{1}{x+1} \ \mathrm{d}x=\ln 2$$  is my answer right ? and are there any other method ?(I'm sure there are)


What is the way to force \includegraphics to use specific file extension for all document?  If I have in the folder figure.pdf and figure.png  \includegraphics{figure} command will use figure.png, if I need *.pdf I could force to use it by typing: \includegraphics{figure.pdf}  But if I need sometimes to compile document with all figures with png extension or pdf, what should I change in graphics package settings?

Can I tell graphicx somehow which graphic format to choose when I omit the file extension in includegraphics and both a PDF and a PNG version of the same image exist? The reason is that I have some very large PDF vector graphics (in terms of file size/drawing primitives) that take a pretty long time to load each time I view the document. I would like to convert them to PNGs while working on the document and only use the PDF versions in the final document. Therefore, a global option that I can switch in the end would be great.  An additional plus would be to do the conversion to PNG on the fly during the LaTeX run if there is a PDF that has not been converted to PNG yet, if a tool for that exists. (I know how to use convert, but not how to include it automatically in LaTeX.)


I am new to shell script and I had the following situation. I have a perl script that has multiple options. Not all the options are required.  example.prl [options] options:      -h             help     -o filename    output file name     -f             force output file overwrite     -d             debug mode     ...   I want to create a shell script to parse the options to the prl script. And the options are not all required, for instance:  ./example.sh -o output_file  OR ./example.sh -o output_file -f   Here is some of my progress but only work with 1 argument:  #!/bin/bash  path=/proj/scripts/example.prl option=$1 option_value=$2  echo "The command to run:" echo $path $name $option  $path $option $option_value    Is there a way to loop through all of the options user put and construct the command?

Currently I'm writing a Bash script which has the following requirements:   it should run on a wide variety of Unix/Linux platforms it should support both short and (GNU) long options   I know that getopts would be the preferred way in terms of portability but AFAIK it doesn't support long options.  getopt supports long options but the  recommends strongly against it:     Never use getopt(1). getopt cannot handle empty arguments strings, or   arguments with embedded whitespace. Please forget that it ever   existed.   So, there still is the option of manual parsing. This is error-prone, produces quite some boilerplate code, and I need to handle errors by myself (I guess getopt(s) do error-handling by themselves).  So, what would be the preferred choice in this case?


How can I replace all the occurrences of the + character in all the filenames in the current working directory with the space character?  I know that there's the linux command rename but I'm not sure how I'd use it to do this.  Example:  Early+Christians -> Early Christians

I have a directory full of images:  image0001.png image0002.png image0003.png ...   And I would like a one-liner to rename them to (say).  0001.png 0002.png 0003.png ...   How do I do this?


With requirement that $A$ precedes the first $B$ which precedes the first $C$.  Example: $AABABCBBAACBCB$ is correct and $BAAACBAACBCBBBB$ is incorrect.   I am thinking of using permutation, get the total number of ways of arranging them and divide the repeat.    There are $14$ spaces, $5$ ways of placing the first one ($5As$), $10$ ways of placing the second one $4As + 6Bs$, but how many ways to place $3rd$, $4th$ and the rest?

I am trying to solve this problem and looking for any tips. I have 5 D's, 6 E's and 3 F's and I have two conditions.  The first D must be before the first E.  The first E must be before the first F.  I thought I could solve this through determining the ways to make a string of letters with a D before an E before an F, however, that is not enough because it does not cover instances like DEFDEF... or DEFFD... since there can be letters that come after the initial string that meets the conditions.  I also contemplated using the Inclusion Exclusion principle as follows  cases where a D comes before an E + cases where an E comes before an F subtract their intersection (which I'm not sure how I'd calculate) however I still cannot account for cases where there are letters after the initial D, E, F...  Any ideas?


I just saw a trailer of 47 Ronin. My first thought was "that doesn't sound right". We have 12 Monkeys and 13 Warriors. Why 47 Ronin? Then I recalled that there is a movie titled Seven Samurai.  I checked the words ronin and samurai with Google, and found that the plural form of ronin can be either ronin or ronins. But the plural form of samurai is samurai.  Is there any guideline on the plural form(s) of loanwords in English, especially those from Japanese?

As someone who has watched a lot of subtitled Japanese animation, it seems odd to hear a word such as ninja (used in the plural) in the dialogue and see it transliterated as ninjas.  It somehow seems better to me to treat ninja just like antelope, bison, buffalo, caribou, deer, elk, fish, grouse, quail, reindeer, sheep, swine, etc., which are both singular and plural.


I am trying to read a text file to my servlet. I thought this statement,  String context = getServletContext().getRealPath("/WEB-INF/rates.txt");   would give me a string of the file contents. My question is: How can I retrieve the file contents into a string? Here is my code:  public void init( ServletConfig config ) throws ServletException {     super.init( config );      String context = getServletContext().getRealPath("/WEB-INF/rates.txt");     ArrayList<CurrencyRate> CR = new ArrayList<CurrencyRate>();      String[] temp = context.split(",\\s*");      for(int i =0; i < temp.length -1; i+=2 ) {         CR.add(new CurrencyRate(temp[i], Double.parseDouble(temp[i+1])));     }      getServletContext().setAttribute( "CR", CR ); }

I've been using the idiom below for some time now. And it seems to be the most wide-spread, at least on the sites I've visited.  Is there a better/different way to read a file into a string in Java?  private String readFile(String file) throws IOException {     BufferedReader reader = new BufferedReader(new FileReader (file));     String         line = null;     StringBuilder  stringBuilder = new StringBuilder();     String         ls = System.getProperty("line.separator");      try {         while((line = reader.readLine()) != null) {             stringBuilder.append(line);             stringBuilder.append(ls);         }          return stringBuilder.toString();     } finally {         reader.close();     } }


The question:  Let $\gamma$ be a contour such that $0 \in I(\gamma),$ where $I$ is the interior of the contour. Show that   $$\int_\gamma z^n \, \text{d}z = \begin{cases} 2\pi i & \text{if }  n = -1 \\ 0 & \text{otherwise} \end{cases}$$  By taking $\gamma$ as the ellipse  $$\{ (x,y) : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \},$$ show that $$ \int_0^{2 \pi } \frac{dt}{a^2 \cos^2 t + b^2 \sin^2 t} = \frac{2 \pi}{ab}.$$  The question's answer uses the Deformation theorem and the fact that the first integral has the given value if the contour is a unit circle. However, the two contours must not overlap, so it seems like this should only be true for a contour that either always has magnitude less than one or greater than one. In Mathematica, the final integral was true for the case that $a = 1.5$ and $b=0.4$. What am I missing?  Edit: The radius of the circle cancels in the integral if $n = -1$, so then it does hold irrespective of the radius.

I want to prove:  $$\int_{0}^{2\pi}\frac{1}{a^{2}\cos^2t+b^{2}\sin^{2}t}dt=\frac{2\pi}{ab}$$  by the deformation theorem of complex variable.  Then I consider a parameterization $\gamma:[0,2\pi]\rightarrow A$, traveled in the opposite direction of the clock hand, of the ellipse (in $\mathbb{C}$):  $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$  I thought of searching for a function $f:A\rightarrow \mathbb{C}$ (analytic in $A$) and a curve $\lambda:[0,2\pi]\rightarrow A$ (homotopic to $\gamma$) and use the deformation theorem:  $$\int_{\gamma}f = \int_{\lambda}f$$  But I can not find a function $f(z)$ that meets what I need, can you help me to find the f?   P.D: Necessarily I have to use the theorem of deformation


I have a situation in which one PC is sitting on top of a roof with a rifle (which I've house ruled as having stats of a repeating crossbow) and there is another PC approaching the building. He wants to literally snipe the other guy in the head as he approaches. Assuming the attack roll hits, is there any way this could be ruled as a 1-hit kill? The player is completely concealed and hidden and all that.  Any advice would be greatly appreciated, I know 4th edition isn't super pvp friendly.

i'm DM to a 4th edition campaign. Been a DM for about 13 years through 2nd and 4th edition and never had to deal with this.  We have a kind of new player into the party, a rogue from PHB1. During combat he kept asking if he could attack the eye of the enemy (Young Blue Dragon) to disable him, or just rip off one of the wings.  Now i know we're in combat, and to get hit in the eye you just need to be very careless or the attacker has to come completely by surprise to achieve something like this.  I can't seem to fond any rule regarding this issue.  The rogue just accepted that he couldn't attack the dragon's eye reluctantly.  Now my question is: Is there any source material addressing this? For now i made a table rule:  If you want to attack a localized spot, the defender cannot know of your existence (invisibility, teleport into battle, etc).  The usual bonus apply, (combat advantage)  If you miss the attack, the defender gets a free opportunity attack with +2 power bonus (aiming and focusing in the attack would be something like range attack, hence combat advantage). This is to prevent possible abuse.  I want to know if this looks like a reasonable rule to deal with this kind of attacks. Or if someone here has more ideas.  Thank you


Is there a way to mass delete compiled list of emails on iOS devices (like can be done in os x)? I only know two options: select individually & swipe "left" and from bottom select "edit", then selecting each message individually. I tried solution described in similar question without success (described as iOS 7).

How do you mass-delete emails in iOS Mail? I don't know if this is documented anywhere, but just to bring it to current attention…


I'm having some problems with orthographic view which I don't know how to solve. Regardless of what mode I'm in (object or edit), I can see through my meshes as if x-ray was on. Rotating my view also causes strange artifacts on my meshes, like in the picture below, and they sometimes disappear entirely until I rotate the view again.  It makes it very hard to work with my meshes in orthographic view, and perspective view does not always satisfy my needs. Is there a way to fix this?

I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks.


I was asked to use the following format for my report in Overleaf  Please use the following set-up within LaTeX:  \documentclass[12pt]{report} \usepackage[y4project]{edmaths}   You can download the style file here:   This is a .sty file,I am not sure how to implement it.  Thanks a lot!  Edit: Error looks like this

Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .


In other words, when a particle's mass increases significantly as it approaches the speed of light (c), does its influence on gravity increase, and if so, does it increase proportionally?

I'm a big fan of the podcast Astronomy Cast and a while back I was listening to a Q&A episode they did. A listener sent in a question that I found fascinating and have been wondering about ever since.   From the show :      Arunus Gidgowdusk from Lithuania asks: "If you took a one kilogram mass and accelerated it close to the speed of light would it form into a black hole? Would it stay a black hole if you then decreased the speed?"   Dr. Gay, an astrophysicist and one of the hosts, explained that she'd asked a number of her colleagues and that none of them could provide a satisfactory answer. I asked her more recently on Facebook if anyone had come forward with one and she said they had not.  So I thought maybe this would be a good place to ask.


I need windows 7 or 8 installed alongside Ubuntu 16.04.  Since I just got the computer, I don't really have any important data on it, so if I lose anything, it doesn't really matter.  Can someone give me a tutorial for dual booting Windows on an Ubuntu 16.04 machine?

I have Ubuntu on my laptop. Now I want install Windows 7 in a dual-boot. How can I do this? I can't lose my Ubuntu files, and I'm afraid that I might break . Go  for UEFI only!


I'm wondering if there is any compact expression to compute (or approximate):  $$\operatorname{Li}_2(pe^{-\alpha})-\operatorname{Li}_2(pe^{\alpha})$$  or  $$\operatorname{Re}\{\operatorname{Li}_2(pe^{-\alpha})-\operatorname{Li}_2(pe^{\alpha})\}$$  The problem is that I cannot use   $$\operatorname{Li}_2(z)=\sum_{n=1}^{\infty}\frac{z^n}{n^2}$$  as for my values, $|z|$ is NOT necessarily less than 1. I am hoping, maybe, having exponential inputs to $\operatorname{Li}_2$ might do some magic. Unfortunately, $p$ and $\alpha$ are pure real. A nice approximation or any piece of advice is greatly appreciated.

I'm wondering whether there any nice identities (or relationships) that can simplify or possibly compact the following expressions:  $$\operatorname{Li}_2(\beta e^{\alpha x}) - \operatorname{Li}_2(\beta e^{-\alpha x}) $$  and  $$\operatorname{Li}_2(pe^{\alpha x}) + \operatorname{Li}_2(qe^{\alpha x}) $$


Does the series $\sum_{n=1}^{\infty}a_n=\frac{1}{n^\frac{1}{n}n}$ converge? I know that I can apply comparison test because this series contains nonnegative members.

Does the following series converge? $$\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$$   As $$\frac{1}{n\sqrt[n]{n}}=\frac{1}{n^{1+\frac{1}{n}}},$$ I was thinking that you may consider this as a p-series with $p>1$. But I'm not sure if this is correct, as with p-series, p is a fixed number, right ? On the other hand, $1+\frac{1}{n}>1$ for all $n$. Any hints ?


When creating a document, I usually build a DVI document because the YAP viewer has a nice feature which allows me to double-click on a word in the DVI document which then causes the source-code window to appear with the cursor on the word (or line) in the source code corresponding to the word in the DVI document where I clicked.  My understanding is that this feature is not available with PDF documents?  Is this correct or can I set up a PDF viewer to cross-reference the source code when I click a word in the PDF document?

Despite having gone through     and having looked at the , there seems to some little changes for TeXnicCenter version 2.0 as of May 2013.  How can I make TeXnicCenter 2.0 to work with Sumatra?


My code looks like this:  $hostname = 'myhost.com'; $database = 'heading'; $username = 'me'; $password = 'pw'; $dbh = new PDO("mysql:host=$hostname;dbname=$database", $username, $password); $dbh->setAttribute(PDO::ATTR_EMULATE_PREPARES, false); $dbh->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION); $sql = "SELECT * from mytable"; $result = $dbh->query($sql)->fetchAll(PDO::FETCH_ASSOC); //var_dump($result); //This works and dumps the array with the right data header('Content-type: application/json'); echo json_encode($result);   This echos nothing back though. No errors, just nothing. If I try echo($result) this echos "Array".   What's happening here?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I have one instance of cases within the align environment, as follows:  \documentclass[a4paper]{article} \usepackage{amsmath} \begin{document} \begin{align} f(x) &=1x \\ g(x) &=\begin{cases} 2 x \label{eq:g_1} \\ 3 x  \end{cases} \end{align} \end{document}   which produces:    How can I number the different cases separately, thus having the numbering (1) for the first equation, (2a) and (2b) for the two cases? Adding a second label within cases as follows  \documentclass[a4paper]{article} \usepackage{amsmath} \begin{document} \begin{align} f(x) &=1x \\ g(x) &=\begin{cases} 2 x \label{eq:g_1} \\ 3 x \label{eq:g_2} \end{cases} \end{align} \end{document}   produces the amsmath package error: multiple \label's. Of course a solution with array instead of cases, or any other alternative, works as well.  Thank you in advance for your help, Basi.

As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&x\geq0\label{positive}\\   0&x<0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result?


I want to execute the specific method of the template if a container has his own find method. For example for set it will execute the first. And for vector the second. Because vector does not have a find method. namespace tools {     template<class TSource, class Ty>     auto exists_in(const TSource &source, const Ty &item)         ->decltype(source->find())     {         return source.find() != source.end();     }      template<class TSource, class Ty>     auto exists_in(const TSource &source, const Ty &item)     {         return std::find(source.begin(), source.end(), item)             != source.end();     } }  int main() {     std::set<int> vector= { 1, 2, 3 };     std::vector<int> set = { 1, 2, 3 };     std::cout<<tools::exists_in(vector, 1);///should execute the first **tools::exists_in** method     std::cout<<tools::exists_in(set, 1);///should execute the second **tools::exists_in** method }

Is it possible to write a template that changes behavior depending on if a certain member function is defined on a class?  Here's a simple example of what I would want to write:  template<class T> std::string optionalToString(T* obj) {     if (FUNCTION_EXISTS(T->toString))         return obj->toString();     else         return "toString not defined"; }   So, if class T has toString() defined, then it uses it; otherwise, it doesn't. The magical part that I don't know how to do is the "FUNCTION_EXISTS" part.


How would you prove the following limit?  $$\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$$  I think the best way is using the squeeze theorem but I can't find left expression.  $$0 \le \frac{x^3y}{x^4 + y^2} \le \frac{x^3y}{x^4} \le \frac{x^3y}{x^3} \le y = 0.$$  But I'm not sure I'm right (especially at $\frac{x^3y}{x^4} \le \frac{x^3y}{x^3}).$  If I'm right - I'd glad if you can accept it.  If I'm wrong - can you please correct me?  Thanks in advance!

How to prove that $\lim_{(x,y) \to (0,0)} \dfrac{x^3y}{x^4+y^2} = 0?$   First I tried to contradict by using $y = mx$ , but I found that the limit exists.  Secondly I tried to use polar coordinates, $x =  \cos\theta $ and $y = \sin\theta$,  And failed .. How would you prove this limit equals $0$?


Mixed Content: The page at '' was loaded   over HTTPS, but requested an insecure image   '...'. This content should also be   served over HTTPS.   I only noticed because I've enabled  for SO and SE.  The issue seems to be the randomly generated gravatars in the "Top Network Askers" sidebar. Notice that the custom ones are being served properly over https.

Gravatar links on the "Top Network Askers" sidebar of the  page are not HTTPS links. Gravatar links elsewhere on the site seem to use HTTPS links.


I am using a Lenovo Yoga 2 Pro with an i7 processor. The Ubuntu download says that it's for AMD64. Will Ubuntu 14.04 work on my device?

Can every CPU (in my case a Intel i7 890) install both of them ? Amd64 and i386 ? I would like to install Ubuntu 64bit. So what is the right download ?


I don't understand which R code I am supposed to be using to figure these problems out. I brief explanation of what the code is doing would be amazing. The problems below are two different applications I'm expected to understand and I don't get either. Thank you!   Problem 1. Let Z~N(0,1) For each of the following, find c such that the equation is true.   a) P(Z<c) = 0.8413  b) P(0<Z<c) = 0.3051  c) P(-c<Z<c) = 0.8664   Problem 2. X~N(3,4) compute  a) P(X>3)  b) P(1<X<8)  c) P(-1.5<X<1)


I have this requirement.  There are a bunch of classes in a package. Each class has constructors. I want to print out all the constructors of those classes in that package.  NOTE: I checked reflections, where it allows to print the constructor names for any class, just at the class level.  try {       Constructor<?>[] publicConstructors = Class.forName("class_name").getConstructors();       System.out.println(Arrays.toString(publicConstructors));     } catch (ClassNotFoundException e) {        e.printStackTrace();     }   But I want to print all the constructors at the package level.  Is this possible? Please help.

Is it possible to find all classes or interfaces in a given package? (Quickly looking at e.g. , it would seem like no.)


Every separable Banach space is isometrically isomorphic to a closed subspace of $C[0,1]$.   I know the result that every Banach space is isometrically isomorphic to a closed subspace of $C(X)$ for some compact Hausdorff $X$. This is proven using Alaoglu's theorem. However, I don't know how to improve this result, replacing $X$ by $[0,1]$.  Any hint will be appreciated!

The theorem is: every Banach separable space can be embedded in $C[0,1]$ linear and isometrically.  I actually found two books which contain the theorem and its proof:  -S. Banach, A Course of Functional Analysis [in Ukrainian], Kiev, 1948.  -L. A. Lyusternik and V. I. Sobolev, A Concise Course of Functional Analysis [in Russian], Nauka, Moscow, 1982.  But I can't read ukrainian nor russian.   Does anyone know a book in english with this proof? The functional analysis books I have read so far don't contain it.  Thank you.


I am trying to create a list and add values to it but getting nullpointer exception. Can you please assist. Below is my Java code:  acctTypeCodes = new ArrayList(); cumBalIndicators.add(new SelectItem("Y", "Y")); cumBalIndicators.add(new SelectItem("N", "N"));   Below is the error from log:  java.lang.NullPointerException     at com.jet.bean.GlAcctRefMBean.getCumBalIndicators(GlAcctRefMBean.java:185)

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 want to prove if the following limit exists, using epsilon-delta definition, or prove it doesn't exist:$$\lim_{(x,y) \to (0,0)}{\frac{x^3-y^3}{x^2-y^2}} = 0$$  My attempt:  First I proved some directional limits, like for $y=mx$ , and $y=ax^n$, and for all of them I got 0. So I conjectured that this limit exists and it's 0. Then I have to prove: $$\forall \delta \gt 0 : \exists \epsilon \gt 0 : \|(x,y)\| \lt \epsilon \rightarrow \left| \frac{x^3-y^3}{x^2-y^2}\right| \lt \delta$$  First I noted that $\frac{x^3-y^3}{x^2-y^2} = \frac{(x^2+xy+y^2)(x-y)}{(x+y)(x-y)} = \frac{x^2+xy+y^2}{x+y}$.  Then I did $\left|\frac{x^2+xy+y^2}{x+y}\right| \leq \left|\frac{x(x+y)}{x+y}\right|+\frac{y^2}{\vert x+y\vert} = \vert x \vert + \frac{y^2}{\vert x+y\vert}$  Using $\|(x,y)\| = \vert x\vert + \vert y\vert$ and assuming  $\|(x,y)\| \lt \epsilon$  $\vert x\vert + \vert y\vert  = \vert x \vert + \frac{ y^2}{\vert y \vert} \geq \vert x \vert+\frac{y^2}{\vert y\vert+\vert x\vert}$  but I can't continue from that since $\vert x + y \vert \leq \vert x \vert + \vert y \vert$ .  I don't know what else to try.

Given is the function $f(x,y)=\frac{x^3-y^3}{x^2-y^2}$ defined for $(x,y)\in\mathbb{R^2}, \, x^2\neq y^2$  I need to find the limit of $\lim_{(x,y)\rightarrow(0,0)} \frac{x^3-y^3}{x^2-y^2}$.   I have tried a few paths, $(x,mx),\, (x,mx^2), \, (x,sin(x)), \, (x,tan(x))$ but all of them yield the same result, $0$.   So I tried to prove the limit exists using the epsilon-delta definition. So: $$\left|\frac{x^3-y^3}{x^2-y^2} - 0\right| = \left|\frac{(x-y)(x^2+y^2+xy)}{(x-y)(x+y)}\right|= \frac{x^2+y^2+xy}{\left|x+y\right|}<\epsilon$$ Here I am stuck and do not know how to proceed.


Problem: A lot of the time I downvote something that clearly shows lack of research or effort on OP's part, and when they edit to improve it, I usually find out pretty late, because there are no notifications to help with that.  Proposition: add a Get notified when this post is edited button/checkbox under a post which you have downvoted (per post, not just all posts ever), so that if there is a significant improvement, you could remove your downvote or even change it to an upvote to show you recognize the improvement.  I believe this would improve public thinking about votes, and make people (who choose to participate like this on the SE sites more often) vote more freely and more often, and everybody else would not think of a <0 post score as a death sentence for their contribution.  I'm not asking to enable this on SO (for a number of obvious reasons), and that's why I propose an opt-in subscription. This would be most useful on lower activity sites like the SE, in my opinion, but who knows.    I want to know if someone has improved their post after a downvote to reinforce the positive behavior and I get -4 on my good intentions? What kind of culture are you trying to cultivate? Please, explain why you disagree without silently downvoting. If you think there's a better way, yes, I want to know your thoughts.

I wonder if it would be possible to extend the current notification system.   Namely, if I downvote a question and that thing had an edit, I'd be happy to see that in my inbox. As possibly the cause for downvote was cleaned up and it should be undone.


I make custom cursors for Tumblr blogs and this was a request, but I can't seem to figure out how to make all but the words transparent; even the spaces in the loops need to be transparent:

I have been given a logo from a client that they want me to 'extract' or 'cut' the text out of and use just the text with a transparent background to fit with the design ethos of their marketing.   I'm using Photoshop CS6 and have tried using channels, magic wand and eraser but I can't get clean edges on the text.  I'm pretty new to Photoshop and any help appreciated.


In the final scene of Predestination there's the following dialogue:     John: Your next attack will kill ten thousand more.   John knows this because it is his strongest motivation for hunting down the fizzle bomber.  Later:     Fizzle Bomber: You wanna know what we're gonna do tomorrow?      John: No.      (John shoots the fizzle bomber)   My questions:  Does the ending cause a paradox because John has supposedly stopped the fizzle bomber from executing his big plan, hence erasing the motivation for the events of the movie? If so, what indicates this?  If not, what signs indicate that the big hit takes place earlier in the fizzle bomber's life, before the laundromat encounter?

In the movie  (2014), does the ending imply that the temporal agent becomes the Fizzle Bomber and therefore a paradox?


My wife and kids are Italian citizens.  Can I visit the UK with my stay permit without a visa?

I'm an Egyptian citizen, who holds Schengen visa and stay permit in Italy. Can I go to UK for some days with my stay permit and Schengen visa?


In "Pragmmatic Programmer" by David Hunt and Andy Thomas, there is a sentence:     Do you ever watch old black-and-white war movies?   To my best english grammar knowledge, present perfect tense should be used here:     Have you ever watched black-and-white war movies?   Is the version of the authors correct? If so, what's the difference between these two variants and what is the appropriate way to use each?  PS. I checked this sentence in the translation of the book in my native language and it was translated exactly as if the orginal sentence was in present perfect form.

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'm looking to create a OD cost distance matrix for a network data set I have created. Is there a way of doing this in QGIS which is akin to Make OD Cost Matrix Layer within ArcGIS's Network Analyst.   My question is similar to  but there was no satisfactory answer given then. That question was asked nearly months ago and am wondering if there is a potential solution.

I'm looking for the steps required to produce an origin-destination (OD) cost matrix.  What I'm looking for is a matrix of road distances. The distance matrix tool only produces euclidian distances. The QGIS Roadgraph plugin produces the shortest road distance from one origin to N destinations. What I need is a file containing distances from all origins to the N closest destinations. I have a lot of origins so repeating the analyses with Roadgraph is not an option. Thanks again.  I'm looking for a step-by-step description, starting from scratch (ie, with my 3 shapefiles: origins, destinations, road network).


I have a div with id="content-area", when a user clicks outside of this div, I would like to alert them to the fact that they clicked outside of it. How would I use JavaScript to solve this issue?

       Display Conents

I have some HTML menus, which I show completely when a user clicks on the head of these menus. I would like to hide these elements when the user clicks outside the menus' area.  Is something like this possible with jQuery?  $("#menuscontainer").clickOutsideThisElement(function() {     // Hide the menus });


I am in high school now and I want to get the basic idea of what relativity. Can anyone suggest me a book or website for it? I am also curious about the mathematics behind it. Is it possible for me to understand relativity in mathematical terms while still in high school? (Let's assume I know everything till Grade 12)

Possible Duplicate:          I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I lack the knowledge behind many of the relativity concepts in the novels. I've always felt curiosity in relativity so I decided that it was the time to buy an introductory book. I went to amazon and checked that there are dozens of "Introduction to general relativity" books in there. So here's my question: What book would you recommend to someone not matematician nor physicist but with (some) mathematical background as an introduction to relativity?


I would like to extract the last and first columns of the following file, which I will call filename.  A   0.400       1.0  1.0      3.0     0.0     1.00  2.0     5.0     1.0   1.00   0.0   0.0  gs100_bs050_rcrs100_rarcinf_core_0400mpc3_df B   0.400       1.0  1.0      3.0     0.0     0.25  2.0     5.0     1.0   0.25   0.0   1.0  gs100_bs050_rcrs025_rarc100_core_0400mpc3_df C   0.03021516  4.0  1.0      4.0     0.0     1.75  2.0     5.0     1.0   1.75  -0.5  -0.5  data_c_rh4_rs175_gs10_ra0_b05n_10k  I tried awk '{print $NF, " ", $1}' filename, expecting to obtain  gs100_bs050_rcrs100_rarcinf_core_0400mpc3_df A gs100_bs050_rcrs025_rarc100_core_0400mpc3_df B data_c_rh4_rs175_gs10_ra0_b05n_10k C  But I obtained instead  A0_bs050_rcrs100_rarcinf_core_0400mpc3_df B0_bs050_rcrs025_rarc100_core_0400mpc3_df C_c_rh4_rs175_gs10_ra0_b05n_10k  on Mac (gawk v 5.0.0) and the same with 3 extra spaces at the beginning of each line on Linux/Ubuntu (mawk 1.3.3). I also tried awk '{printf("%s  %s\n", $NF, $1)}' filename, but got   A100_bs050_rcrs100_rarcinf_core_0400mpc3_df  B100_bs050_rcrs025_rarc100_core_0400mpc3_df  Cta_c_rh4_rs175_gs10_ra0_b05n_10k  on Mac. Since the longest string of the last column is 45 characters long. So I then tried:  awk '{printf("%-50s  %s\n", $NF, $1)}' filename, but this returned       As050_rcrs100_rarcinf_core_0400mpc3_df       Bs050_rcrs025_rarc100_core_0400mpc3_df                 Cgs10_ra0_b05n_10k  My example fits in the awk limits of 1024 characters per field and 100 fields. Could this be a bug in awk?

I'm trying to add a column to a csv file by using:  awk -F "," '{print $0"new_col"}' file.csv   but I got :  new_col8,0.405,0.101 new_col4,0.374,0.100 new_col23,0.342,0.100 new_col130,0.298,0.100   instead of :  68,110,0.362,0.101,new_col 11,98,0.405,0.101,new_col 57,94,0.374,0.100,new_col 61,123,0.342,0.100,new_col 124,130,0.298,0.100,new_col   I tried like this too:  awk -F "," '{{$(NF+1)=",new_col"} print $0 }' file.csv   but i got the same result!!!  Is someone already had this problem?


How do I explain zero knowledge proof to my 7 year old cousin?

Alice is color blind.  She never knows if her gloves are matched.  Her   brother Bob always   teases her saying her gloves are mismatched and   she should go change them.  Alice wants to  know if Bob is telling the   truth about her gloves.      Assuming Alice only has 2 colors of gloves, how can she design a   protocol that she can use  with her brother to determine if Bob is   being truthful or just teasing her?   I would assume that Bob decides at the beginning whether to tease or be honest. If teasing, he chooses his response at random.  My intuition tells me this problem is similar to the coin toss over the phone problem... but I can't seem to create a scheme where Alice would know if he was telling the truth is she has no way of verifying?  Any help would be appreciated as I'm studying for finals!


General relativity assumes that space itself is warped by gravity, which is what gives rise to the shapes of the paths followed by objects subject to a gravitational field.  If space itself truly bends, then the paths of all particles in an area of space warped by a gravitational field should be affected.  As a result, the path of the force carrier of an electrostatic field should also be affected by the presence of a gravitational field, since the path of that force carrier should also be affected by the local warping of space.   Therefore, any electrostatic field that is within an area of space warped by a gravitational field should in some way be affected the presence of the gravitational field.  If so, has the effect been measured by experimentation?

Suppose we have a pointed electric charge or a bipolar magnet. If we put a massive gravity source nearby, will the magnetic and electric fields be distorted? In what way?


Is it possible to detect if a custom environment goes over a page break, i.e. get a warning/something I can use for further processing (and preferably also tells me where the page break occurs)?  \newenvironment{Test}{\CheckIfPageBreak\PrintPageBreak}{}   In document:  \begin{Test} A A A A \end{Test}   results in   False A A A A   while  \begin{Test} A A /--page break due to long text--/ A A \end{Test}   results in   True A A /--page break--/ A A

Based on my question  my setup is currently looking like:  \newenvironment{A}{\label{env:A}}{} \newenvironment{B}{ %%Pseudocode \if\thepage!=\pageofref{env:A} Pagebreak happened! \fi %% End Pseudocode }{}  \begin{A} Text \begin{B} SubText \end{B} \end{A} \begin{A} Text2 \begin{B} SubText2 \end{B} \end{A}   My problem now is that I am basically reusing the label defined the first time. Is there a way to set the label-check in environment B to check the label which was created by the current environment A, and not any labels created earlier?


In a game show a contestant selects one of three doors:   Behind one of the doors there is a prize and behind other two there is no prize. Each door has equal probability of having a prize. After contestant selects a door, the game show host who knows what's behind each of the doors, deliberately opens one of the remaining doors and reveals there is no prize behind it. The host then asks the contestant whether he want to $\text{SWITCH}$ his choice to other unopened door or $\text{STICK}$ to his original choice.  Which of the following options is/are correct ?: $(1)$ Probability of winning the prize is same whether contestant $\text{STICK}$ or $\text{SWITCH}$ $(2)$ Probability of winning the prize when contestant $\text{STICK}$, is Image not present $(3)$ Probability of winning the prize when contestant $\text{SWITCH}$, is Image not present $(4)$ It is advantageous for contestant to $\text{SWITCH}$ than to $\text{STICK}$ The solution to this question is $(2)$, $(3)$, $(4)$ But according to me the solution should be only $(1)$ because the probability should be same for both the cases, either he $\text{SWITCHES}$ or $\text{STICKS}$ to his choice. Can anyone explain.

I'm confused about why we should change door in the Monty Hall Problem, when thinking from a different perspective  gives me equal probability.   Think about this first: if we have two doors, and one car behind one of them, then we have a 50/50 chance of choosing the right door.   Back to Monty Hall: after we pick a door, one door is opened and shows a goat, and the other door remains closed. Let's call the door we picked A and the  other closed door B. Now since 1 door has already been opened, our knowledge has changed such that the car can only be behind A or B. Therefore, the problem is equivalent to: given two closed doors (A and B) and one car, which door should be chosen (we know it's a 50/50 thing)? Then, not switching door = choosing A, and switching door = choosing B. Therefore, it seems that switching should be equally likely, instead of more likely.   Another way to think: no matter which door we choose from the three, we know BEFOREHAND that we can definitely open a door with a goat in the remaining two. Therefore, showing an open door with a goat reveals nothing new about which door has the car.   What's wrong with this thinking process? (Note that I know the argument why switching gives advantage, and I know experiments have been done to prove that. My question is why the above thinking, which seems legit, is actually wrong.) Thanks.


I was wondering will I get a compensate if the screen was not working the entire flight from London to LA through the British airlines? I did report the issue.

In long haul flights, if I get a seat and after take off I found out that entertainment system is not working, I asked a flight attendant to change my seat but she apologized because there are no empty seats to move to.   Is it common to ask for a compensation for such an inconvenience? do major airlines compensate you in such cases?


In many textbooks, the interval  $$ I = -(c\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 $$  is taken for granted as the same for two events in any reference frame.  Is it possible to derive this just from the two postulates,   That the laws of physics are the same in all reference frames That the speed of light c is constant for all reference frames?

What's the cleanest/quickest way to go between Einstein's postulates [] of   Relativity: Physical laws are the same in all inertial reference frames. Constant speed of light:  "... light is always propagated in empty space with a definite speed $c$ which is independent of the state of motion of the emitting body."   to Minkowski's idea [] that space and time are united into a 4D spacetime with the indefinite metric  $ds^2 = \vec{dx}^2 - c^2 dt^2$.  Related to the question of what is the best derivation of the correspondence are: Is the correspondence 1:1? (Does the correspondence go both ways?) and are there any hidden/extra assumptions?    Edit  Marek's answer is really good (I suggest you read it and its references now!), but not quite what I was thinking of.   I'm looking for an answer (or a reference) that shows the correspondence using only/mainly simple algebra and geometry. An argument that a smart high school graduate would be able to understand.


I want to use a DLL library for Win32 in Linux.  Can I use a library of Wine to do that?

We need to interface to 3rd party app, but company behind the app doesn't disclose message protocol and provides only Windows DLL to interface to. Our application is Linux-based so I cannot directly communicate with DLL. I couldn't find any existing solution so I'm considering writing socket-based bridge between Linux and Windows, however I'm sure it is not such a unique problem and somebody should have done it before. Are you aware of any solution that allows to call Windows DDL functions from C app on Linux? It can use Wine or separate Windows PC - doesn't matter. Many thanks in advance.


I have quick look but I do not seem to find the answer to the following question. Basically, I get the following output when I run lm():      Call: lm(formula = y ~ as.factor(x1) * x2, data = data)  Residuals:      Min       1Q   Median       3Q      Max  -13.7237  -3.4391   0.8872   3.7576   8.3555   Coefficients:                                Estimate Std. Error t value Pr(>|t| (Intercept)                  8.448e+01  1.646e+00  51.318   <2e-16 *** as.factor(x1)2               5.273e-01  2.967e+00   0.178   0.8597     as.factor(x1)3               2.442e+00  2.542e+00   0.961   0.3416     x2                          -3.259e-05  8.820e-05  -0.369   0.7134     as.factor(x1)2:x2           -2.641e-04  2.636e-04  -1.002   0.3215     as.factor(x1)3:x2           -2.728e-04  1.314e-04  -2.076   0.0434 *  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Residual standard error: 5.809 on 47 degrees of freedom   (2 observations deleted due to missingness) Multiple R-squared:  0.207, Adjusted R-squared:  0.1227  F-statistic: 2.454 on 5 and 47 DF,  p-value: 0.04683   The question is what is the interpretation of regression coefficients? More specifically what do the estimates of interaction mean? For example, is  -2.728e-04 the interaction term or the effect of x2 on (x1)3?  Thank you very much in advance!

I have a model: $$ \ln({\rm earnings}) = a+b_1{\rm female}+b_2{\rm white}+b_3{\rm female}\times{\rm white} $$ ${\rm female}$ and ${\rm white}$ are dummy variables.  I have interpreted $b_1$ and $b_2$:    $b_1$ = change in female earnings comparing to male given you are non white $b_2$ = change in white earnings comparing to non white given you are male   But I am unable to interpret the coefficient of the interaction term ($b_3$). Please help me with this.  Let me make it more clear what I need out of this regression $$ \ln({\rm earnings}) = 2.618656-.0899657{\rm female}+.382019{\rm white}-.2754126 {\rm female}\times{\rm white} $$ Now i know there is gender pay difference with b1, i also know there is race pay difference with b2. Now with b3 i need to know is their a gender pay gap for whites only. How can i figure that out with regression above and without test.


I am trying to make a python script but cant get it to work right. I am dealing with very small numbers and python doesn't seem to like it. Here is my script:  x = 0 while x < 3:     x += .0001     if x == 2.5:         print "X is now: ", x         break     else:         print x   When I run it in PyCharm I get this output (I've shortened it so you don't have to scroll through a bunch of numbers.)  2.4988 2.4989 2.499 2.4991 2.4992 2.4993 2.4994 2.4995 2.4996 2.4997 2.4998 2.4999 2.5 2.5001 2.5002 2.5003 2.5004 2.5005 2.5006 2.5007 2.5008 2.5009 2.501   Pycharm is acting as if my "if" statement doesn't exist. It skips right over the number 2.5 without running  if x == 2.5:     print "X is now: ", x     break   I figured it's something to do with the way my computer is running those numbers and the 2.5 i'm seeing is really 2.5000001 or something but I don't know. I've tried putting the numbers into scientific notation hoping it would help but instead I get the error "Too much output to process"  I'm fairly new to python and am starting to get annoyed by this. Any and all help it appreciated. Thanks.

Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


In a Windows batch file, is it possible to get the text of date in some location independent form to get the location independent date stamp as a string? To make the question clear... In the Czech Windows, the wanted code looks like this:  d:\>date /t čt 16. 05. 2019  d:\>echo %DATE:~-4%%DATE:~-8,2%%DATE:~-12,2% 20190516   However, in the English Windows the same code returns bad results for obvious reasons:  d:\>date /t Thu 05/16/2019  d:\>echo %DATE:~-4%%DATE:~-8,2%%DATE:~-12,2% 2019/1u   If the code is tuned for the English Windows, then it does not work in the Czech environment. How it should be implemented?

Update: Now that it's 2016 I'd use PowerShell for this unless there's a really compelling backwards-compatible reason for it, particularly because of the regional settings issue with using date. See @npocmaka's     What's a Windows command line statement(s) I can use to get the current datetime in a format that I can put into a filename?  I want to have a .bat file that zips up a directory into an archive with the current date and time as part of the name, for example, Code_2008-10-14_2257.zip. Is there any easy way I can do this, independent of the regional settings of the machine?  I don't really mind about the date format, ideally it'd be yyyy-mm-dd, but anything simple is fine.  So far I've got this, which on my machine gives me Tue_10_14_2008_230050_91:  rem Get the datetime in a format that can go in a filename. set _my_datetime=%date%_%time% set _my_datetime=%_my_datetime: =_% set _my_datetime=%_my_datetime::=% set _my_datetime=%_my_datetime:/=_% set _my_datetime=%_my_datetime:.=_%  rem Now use the timestamp by in a new ZIP file name. "d:\Program Files\7-Zip\7z.exe" a -r Code_%_my_datetime%.zip Code   I can live with this, but it seems a bit clunky. Ideally it'd be briefer and have the format mentioned earlier.  I'm using Windows Server 2003 and Windows XP Professional. I don't want to install additional utilities to achieve this (although I realise there are some that will do nice date formatting).


I know that gluing opposite sides of a square gives a torus, and I think I've seen somewhere that gluing opposite sides of an octagon gives a 2-holed torus.  Is there a general way of constructing gluing diagrams for surfaces of genus $g$ / for $k$-holed-tori?

I came across the problem of computing the homology groups of the closed orientable surface of genus $g$.   Here  I found a solution via cellular homology. This seems to me like the natural way of calculating something of this sort although I know that it is also possible to do this using the Mayer-Vietoris sequence.  I understand the main calculations of the solution referred to above, however the CW-structure that the surface of genus $g$ is endowed with is a mystery to me.  I understand it for the case $g=1$ where it is quite conceivable in a graphic manner.   Could someone please explain what is going on for $g \geq 2$?  Thanks in advance for any help.


I have been trying to set a 301 redirect from a non www to a www domain since yesterday but it only cause problems on my site. I first tried it from the control panel of the website, then by modifying the .htaccess file with the following:  Options +FollowSymlinks RewriteEngine on rewritecond %{http_host} ^example.com [nc] rewriterule ^(.*)$ http://www.example.com/$1 [r=301,nc]   My site is based on wordpress, the first problem that occurred was that I could not access my backend anymore… when I was trying to log in the page would just reload itself and then there was an endless loop and the whole site was unaccessible. After removing these few lines, everything was fine.

This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not.


I have a new MacBook Air and I keep bumping the caps lock key. As you can imagine this is really frustrating.   Is there a way to totally disable the caps lock key without having to install software or mucking around with Terminal?

Is there any way to completely disable the caps lock key without using any third-party apps?  (Virtually, of course—I don't plan on jamming something under the key.)


About graphic designer positions where it needs to know HTML and CSS, what are all the projects one needs to be able to do with HTML and CSS in order to be employable?

As a web developer, both front-end and back end architect, I work with many different designers and sometimes find it frustrating working with design comps where no thought was put into how to accomplish the design in basic CSS and HTML.  On the other hand as a developer I'm expected to be able to produce code from any design.  Do web designers need to know basic modern CSS and HTML techniques?  Why or why not is this important for a well rounded web designer?  Some general thoughts:   Front end web developers should be skilled enough to code up any design. Web designers should have an understanding of how users will actually interact with their design. Design shops would rather have designers design and leave all the coding up to the developers.


What do you do when someone asks a question on a Stack Exchange site and that person clearly has not even attempted to google the answer? Downvote it? Something different?

A user walks into Stack Overflow and . The answer for his question is in the first result of a Google search. Well, it is the fourth result, to be precise, but the first link in the discussion under the first link leads there anyway.  Long story short: the question is very simple and the answer is two clicks away in Google. What should I do? Should I give user the link to answer or should I point him to the Google Search results? What is Stack Overflow, a place to learn something (even if it is googling) or a black box "insert question, receive answer" machine?  (Meta Stack Overflow's policies prevent me from posting a link to Google? WTF.)


Show that if $u$ is harmonic in $\mathbb{R}^n$ and $u = o(|x|)$, then $u$ is constant.  I am trying to prove this result by the mean value property. But it doesn't work. Please help me. Thanks!  PS: I just realized that one can prove it easily by the estimates on the derivatives of harmonic functions, which implies a stronger result:   If $u$ is harmonic in $\mathbb{R}^n$ and $u \le C(1+|x|)^N$, then $u$ is a polynomial of degree at most $N$.   But I am still curious about how to prove it directly by the mean value property, which is the "Hint" for this problem.

Show that if $u$ is harmonic in $\mathbb R^n$ and $u=o(|x|)$, then $u$ is a constant.(Hint: use the solid version of the mean value property $u(x)=\frac{1}{\omega R^n} \int _{B_{R(x)}} u(y)dy$, and estimate $|u(x)-u(x')|$.)  Can anyone tell me how to use this hint?


Let G be a region and deﬁne $G^∗ = \{z : z̅ ∈ G\}$. If $f : G \to \mathbb{C}$ is analytic, prove that $f^* : G^∗ → C$, deﬁned by $f^*(z) = \overline{f(\overline{z})}$ is also analytic.

So I'm working a problem that states:     A function $f$ is analytic in an open set $U$. Define $g$ by $g(z)=\overline{f(\overline{z})}$ (just because the notation can be hard to read, this is the the complex conjugate of the function $f$ defined at the complex conjugate of $z$). Show that $g$ is analytic in the oopen set $U^{\star}=\{z:\overline{z}\in{U}\}$ and that $g^{\prime}(z)=\overline{f^{\prime}(\overline{z})}$ (this is the complex conjugate of the derivative of $f$ evaluated at the complex conjugate of $z$) for $z\in{U^{\star}}$   Now, my book gives the definition of an analytic function as one that is a function defined over an open set on which it is differentiable at every point of that set and that every derivative of that function satisfying the preceeding properties has derivatives that are analytic on that domain as well.  So, I know that being differentiable at a point means that a function is continuous at that point, so I see straight away that this means $\forall{\epsilon}>0$ there exists a $\delta>0$ such that if $|z-z_0|<\delta$ then $|f(z)-f(z_0)|<\epsilon$. Since $U$ is an open set, it follows that $U\cap{z_0}$ is non-empty. Because $f$ is analytic in $U$, I can choose two elements $z$ and $z_0$ of $U$ that satisfy $|z-z_0|=|\overline{z}-\overline{z_0}|<\delta$ and  $|f(z)-f(z_0)|<\epsilon$. Since $|\overline{z}-\overline{z_0}|<\delta$, this means that $|f(\overline{z})-f(\overline{z_0})|<\epsilon$. Observing that $|f(\overline{z})-f(\overline{z_0})|=|\overline{f(\overline{z})-f(\overline{z_0})}|$, I conclude that $\overline{f(\overline{z})}$ is continuous.  This being the case, then (and I think I've done this part correct) I can compute the derivative by using the limit definition as:  $g'(z)=\lim\limits_{h\rightarrow{0}}\frac{\overline{f(\overline{z}+\overline{h})}-\overline{f(\overline{z})}}{h}=\lim\limits_{\overline{h}\rightarrow{0}}\overline{({f(\overline{z}+\overline{h})-f(\overline{z})})\ \  /\ \ {\overline{h}}}$, as I know that as $h\rightarrow{0}$, so does $\overline{h}\rightarrow{0}$. Since the function $f$ is analytic for all complex numbers in $U$, its derivative there, as given above, is the complex conjugate of the limit which is $\overline{f'(\overline{z})}$.  That's what I'm concerned about, however, because I haven't actually shown yet that $\overline{f(\overline{z})}$ is, in fact, analytic on its domain, all I know is that it is continuous on its domain. My thought is that it might only be analytic for the set $U$ if $U$ is a subset of the real numbers, since that is the only place that $\overline{z}$ is analytic and thus the composition $(a\circ{b})(z)$ for $b(z)=f(\overline{z})$ (analytic for $\overline{z}\in{U}$) and $a(z)=\overline{z}$, so the composition would be analytic on the set given by the intersection of the real numbers with $U$ but I don't believe that is right?  I've tried considering an equivalent case given by the conjugation $\overline{g(z)}=\overline{\overline{f(\overline{z})}}=f(\overline{z})$ to no avail.  Essentially, I'm asking to see if anyone can point me in the right direction and tell me if what I've done so far is on the right track.  I should add that these problems are from a section in the book preceeding the discussion about the Cauchy-Riemann Equations, so while I'm not sure if they will help, I don't want to use them.  I'm tagging this as homework although it's not 'homework' in the sense that I'm taking a class, but the problem is from a book, so I feel it is appropriate to tag it as such. I invite any admins to remove the tag if they feel it is unnecessary.


This issue happened after running updates. I've checked the system but only one Nvidia driver seems to be present. Purging / reinstalling the Nvidia drivers didn't fix it. Nor did purging / reinstalling the snap system. Could it have something to do with nvidia-prime? How does it check for the issue?

I have located where the error message originates from it is in  line number 221. As I have only a single nvidia driver installed I suspect it is is the same issue. I am not a developer but looking at the code preceding this line I can see the statement.  const char *glob_pattern = "/usr/lib/nvidia-[1-9][0-9][0-9]"  this will pick up nvidia-352/ nvidia-361/ and nvidia-361-prime/ ? on my PC.


We reached the station on time.      We reached the station in time.   I think first one means we reached at particular point of time when we are required to reach.  And second means we reached before the required time.  Am I right? Or is there any other difference or meaning? If so, Please explain to me. And please explain me the points of grammer related to this.

I have an appointment at 8 and I arrive there at 7:55, is it "on time" or "in time"? What about "the nick of time"?


When a druid uses its  feature:     Your game statistics are replaced by the statistics of the beast, but   you retain your alignment, personality, and Intelligence, Wisdom, and   Charisma scores. You also retain all of your skill and saving throw   proficiencies, in addition to gaining those of the creature. If the   creature has the same proficiency as you and the bonus in its stat   block is higher than yours, use the creature's bonus instead of yours.   Consider the example of a Circle of the Moon druid, who does not have proficiency in Stealth, taking the form of a . A saber-toothed tiger's statblock states that it has a +6 modifier to Stealth. Since the beast's Dexterity modifier is +2, and a CR 2 beast has a proficiency bonus of +2 (), the saber-toothed tiger must have double proficiency in Stealth.  Should the druid therefore double their proficiency bonus and add it to the saber-tooth tiger's Dexterity modifier, resulting in the wild-shaped druid having +8 to Stealth at level 6, +10 to Stealth at level 9, etc.?

The PHB entry on Wild Shape states: "You also retain all of your skill and saving throw proficiencies, in addition to gaining those of the creature."  Does this mean you add the character's Proficiency Bonus to the beast's physical attribute modifiers to arrive at the Skill total? For instance, my Druid has a PB of +3, proficiency in Stealth and an 18 Dex, for a total of +7 Stealth in normal form. But in Polar Bear form, her Dex drops to 10...does that mean I'd only be at +3 in Stealth in bear form?


For induction motors, which type of connection, star or delta, is used in the stator winding and the rotor winding and why?

I have been studying three-phase systems for the whole course of a subject (on the first year of the university degree). I have finished now, and I know both "Y" (star) or "Delta" (triangle) connections. I have made a lot of computations with them, however I don't know the different applications they have and I would like to know the following in order to increase my knowledge.  I would like to know which one is better (Y or Delta) for different purposes, they must have its advantages and disadvantages, but I have never been told which ones are them. I have tried to do some research on the Internet, but I haven't found in particular a good answer. I have only seen the advantages and disadvantages of Y and Delta motor startup, but I'm thinking more of the "circuit" point of view.  I'm really interested on the subject, but I just seen it from the computational point of view. I would appreciate if someone could explain me a little bit some of the main advantages and disadvantages of using both connections. Thank you.


I am trying to write a method that receives two arrays and concatenates them. Right now I am getting the error "Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 2." I do not understand why this is happening. Can someone explain why I am getting this error?   public static int [ ] concat (int [ ] nums1, int [ ] nums2)      {         int length = nums1.length+nums2.length;         int nums3 [] = new int [length];         for (int i=0; i<nums1.length; i++)         {             int value = nums1 [i];             nums3 [i]=value;         }         for (int i=0; i<(nums1.length+nums2.length); i++)         {             int value=nums2 [i]; //It says I have an error on this line but I do not understand why.          length = nums1.length+1;             nums3 [length]= value;         }         return nums3;      }

I need to concatenate two String arrays in Java.  void f(String[] first, String[] second) {     String[] both = ??? }   What is the easiest way to do this?


I am from India and will be preparing for RMO (Regional Mathematics Olympiad) and INMO (Indian National Mathematics Olympiad). I need the best books for being able to qualify these and appear for IMO.

I am preparing for Mathematics Olympiad , can any one suggest me some books to prepare for olympiad ? The topics that usually come up involve:    congruence modulo $n$,  inequalities , number system, elementary number theory, etc.   Please help me!  Thanks  Kushashwa


How do i solve this problem?  $\frac{-1}{3}|6−5x|+2<1$  so far I took the 2 to the other side, multiplied both sides by -3 to cancel out the -1/3  leaving me with $|6-5x|>3$  is this correct? by flipping the signs since i multiplied by a negative?but then what?

How do I solve these? $$|-2w-4|<12$$  and  $$(-1/3)|6-5x|+2<1$$  for the first problem i got $-8<w<4$ is that right?