Given is category Set Given two objects from this category, $A$, and $B$, which are sets without any other structure, there is an arrow $f: A \to B$, from $A$ to $B$, which is any total function from $A$ to $B$.  For given set $A$, there is ( by axiom of CT ) identity arrow $1_A$ .  Then it looks like identity arrow may be a permutation...  Buy identity arrow for a given object has to be unique. And there is many permutations for given set $A$.   So do we have here "equivalence class" of identity arrow?

I've been trying to wrap my head around the basic concepts of category theory, and I thought I would attempt to illustrate what I understand with the category of sets, probably the easiest example. Particularly, I've been trying to prove that $id_A$ (the identity morphism on $A$, for all $A \in Obj(\mathbf{Set})$) is $1_A \colon A \rightarrow A, x \mapsto x$.  This is a very intuitive and reasonable statement, and it's trivial to prove that $1_A$ is indeed an identity morphism on $A$, and I suppose uniqueness of $id_A$ can be demonstrated analogously to uniqueness of the identity element in a monoid (considering the subcategory which has $A$ as its only object, and endofunctions on $A$ as its only morphisms).  In this manner, it is not hard to prove that the proposition in the title is true, but this demonstration requires to make an assumption or guess as to what could $id_A$ be. Specifically, the scheme of the proof is: assume $id_A$ = $1_A$, see that it works with the definition of an identity morphism, show that the identity morphism is unique, and, in conclusion, $id_A$ can only be $1_A$. What I'm looking for, nonetheless, is a somehow more direct proof, that doesn't assume $id_A$ = $1_A$ at the start. I want to place myself in a state of little or no knowledge about sets and functions, and under this assumption, why would I assume $id_A$ = $1_A$ at first? Why not try with $id_\mathbb{Z}$ = $f \colon \mathbb{Z} \to \mathbb{Z}, x \mapsto x^2 + 1$, for example? It wouldn't work, but I don't have any reason to think that $1_\mathbb{Z}$ is a better guess for $id_\mathbb{Z}$.  I suppose that the proof for which I'm asking would work for categories of sets with additional structure, and probably for posets as well, although I'm not clear as to what modifications it would require to work.  Thanks.


When a recipe calls for sugar and oil or butter which one can applesauce be substituted for and what is the ratio?

In many recipes, mostly desserts, it is suggested that you can substitute oil with applesauce to reduce the fat content. But why applesauce?  Is there something special about applesauce or are there other ingredients than can be used?


Summary of Issue: The Edge Lengths are inconsistently displayed on an obviously square object. Issue Detail: I'm still quite new to Blender. Iam busy creating door frames using Cube, boolean difference, deleting the inner faces, capping the inner faces, and finally extruding the door frame out. However, I've noticed some strange behavior. I'm sure this is by design, but it seems to have caused me problems now. What I initially did was extrude, and type the measurement I wanted (0.004) for the door frame faces. However, I realized that I actually needed to set it to 0.04 instead. So instead of extruding again, I selected the faces and used the Move tool to specify my new measurement numerically (0.04) and hit enter. It seems however that it appends the measurement using some unknown logic which doesn't make sense to me. The side effect that I'm dealing with now in order to try regain consistency using "Edge Lengths" is that the edges of what is seemingly a square, is actually of different lengths. I have no idea what is going on, however I can only find help on this for Blender 2.8, and apparently the entire application UI changed within a single minor version number. Please may somebody help me out here. This is what I'm talking about:

I just found out about the Mesh Display : Length feature in the "N" panel (thanks to ) that allows one to measure the length of a face or vertice.  But my first encounter with this tool gives me complex feelings of love and hate, see how, as I was trying to measure the aspect ratio of this TV screen, I am getting WIDTH = 20.33 and HEIGHT = 37.57.  These values seem awfully wrong, since my betrusted eyes tell me the height should be shorter than the width.    I have tried measuring the single vertices as well, to identical results.


I swear I read such a word once, as does my partner; but no amount of Googling has been able to suss it out:  I’m looking for something that means “to extinguish a family tree,” in the sense of complete genetic extinction; to hunt down and kill all members of someone’s extended family.  (Dark, I know!)

I would like to know if there is a word or phrase for a systematic campaign to annihilate every descendant of a particular ancestor.   We have the word 'genocide' for killing off an entire race, and plenty of words for killing people based on how they are related to you (fratricide, filicide, et. al.), but looking over the  and the , I couldn't find a term for systematically killing an entire bloodline.   My question is prompted by a US news story about the horrific murder of 8 members of the same family, but those murders are not an example of what I'm thinking of because the children of the victims were left alive, so the motive for the killings was not to kill off the bloodline. The sense that some group had coordinated an attack against just one family is what made me wonder what the "not an entire race, just one bloodline" version of 'genocide' would be called.   Searching the Internet for "kill off" and bloodline sends me straight into the land of vampires, Illuminati, reptilian overlords, and, naturally, Priory of Sion nonsense so I haven't had much luck finding a thread to pull.   It may be that there is no word for it in the sense of murdering a human bloodline, because we just don't attempt kill off our royals down to the last heir often enough to coin a term for it. Maybe there is a scientific term for culling a line from a test population as part of biological research?


I have a question about ARM processors and thermal monitoring. I tried asking on Server Fault but it got closed as off topic. It certainly isn't a Stack Overflow question.   Where should I ask this type of questions?

Recently I wondered about a webcam on my laptop; about the driver problem with it and about all stuff related to devices and hardware. I see, that the Stack Exchange network has Q&A about: programming and servers mostly, but what about hardware specifically? Is there or will there be a Stack Website just for hardware? About: HDD, RAM, CPU, motherboards, graphic cards, etc.?  I hope I don't repeat an already asked question, but since there is no distinct answer for it I asked it as I see it.


I understand the capitalization rule for nouns, proper nouns require a capital letter. Also, I should begin a new sentence with a capital letter.  When & why "mom/dad" requires a capital letter ?  (Reference- ELL- )     mom:      (n) informal term for a mother/North American term for mum.

I am trying to understand capitalization rules with Mom and Dad. I believe I have it correct below, but please let me know if I do not.     The one thing I learned from my dad was that it was good to earn the trust of one's children. Dad has shown me how good that a dad can be. One day when I went to his house, and Dad wasn't there, I ran outside....   The above passage is just made-up just so that you would see what I mean about capitalization. Let's put numbers by each one, like so:     The one thing I learned from my dad(1) was that it was good to earn the trust of one's children. Dad(2) has shown me how good that a dad(3) can be. One day when I went to his house, and Dad(4) wasn't there, I ran outside....    This is one where I'm not certain. I believe in this sense I'm showing possession here with "my", and it just didn't seem right saying "my Dad". I don't know what the grammar rule is here, or if I even have it right. This one is obvious—it starts the sentence. In this case, I'm using Dad like a name instead of saying "Larry". Therefore, it should be capitalized. Again, just like 3.


A regular occurrence in updating Ubuntu is kernel updates, which require a restart. There are applications which negate the need for a restart after a kernel update e.g. ksplice.  Why doesn't Ubuntu use tools similar to ksplice? Are there security, memory, etc. concerns to not restarting immediately/ever? Or, can these issues be overcome (i.e. are they just bugs)?

Ksplice is an amazing software (or whatever it is). It changes the way kernel updates work: Instead of rebooting after an update, it patches memory, so you don't need to do anything.


Puzzle: In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?      Answer given: If the lily patch is covering the pond fully on day 48, and it's doubled in size that means you only have to go back one day to when it was covering half the pond. So on day 47, the lake is half full.     I have my doubts about the answer and I was wondering how to mathematically get to the answer.    Found in an article of the .

A lily pad doubles in area every second. After one minute, it fills the pond. How long would it take to quarter fill the pond?   To me this seems like we can set up a fraction-like equation:  $$\frac{60 \ \text{seconds}}{1} = \frac{x \ \text{seconds}}{1/4}$$ then $x = 15$ seconds. But the answer is $58$ seconds which really makes no sense to me. Any suggestions are greatly appreciated.


I have two computers, let's call them A (192.168.0.10) and B (192.168.0.11). I want A to ping B. However, A cannot ping B unless B pings A first.  # computer A $ ping 192.168.0.11 # result: Destination Host Unreachable  # computer B $ ping 192.168.0.10 # result: works # 64 bytes from 192.168.0.10: icmp_seq=20 ttl=64 time=1.76 ms  # computer A (after computer B pinged A) $ ping 192.168.0.11 # result: works # 64 bytes from 192.168.0.11: icmp_seq=1 ttl=64 time=2.65 ms   Do you have any idea what happens? Because of this behavior I cannot ssh the computer before B pinged for example.  This happens in my WLAN.

I have two OSX machines on a local subnet.  Pings from Machine A to Machine B consistently timeout until Machine B pings Machine A.  After B pings A, A can successfully ping B, but this success is temporary; if there is no communication between the two machines for a half hour or so, pings from A to B begin timing out again (until B pings A again).  How can I ensure that B is always reachable from A, without having to "kickstart" the connection by pinging A from B first?


i have recyclerview in my App and when list item is pressed bottomsheet dialog expends where i have two buttons but i can't set click listeners to it. This is onClick method in adapter  BottomSheetDialog offer_info_dialog; RelativeLayout rel; Button Yes,No; View parentView; @Override public void onClick(View view) {     rel = (RelativeLayout) activity.findViewById(R.id.bottomsheet);     Yes = (Button) offer_info_dialog.findViewById(R.id.confirm_btn_on_info);     No = (Button) offer_info_dialog.findViewById(R.id.cancel_btn_on_info);         offer_info_dialog = new BottomSheetDialog(context);         LayoutInflater inflater = (LayoutInflater) context.getSystemService( Context.LAYOUT_INFLATER_SERVICE );         parentView = inflater.inflate(R.layout.offer_info_layout, null);         offer_info_dialog.setContentView(parentView);         ((View) parentView.getParent()).setBackgroundColor(context.getResources().getColor(android.R.color.transparent));         offer_info_dialog.show();         rel.setVisibility(View.INVISIBLE);      Yes.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View v) {             MainActivity.removeCheatOfferMarkers(2);         }     });      No.setOnClickListener(new View.OnClickListener() {         @Override         public void onClick(View v) {             BottomSheetBehavior bottomSheetBehavior = BottomSheetBehavior.from((View) parentView.getParent());             bottomSheetBehavior.setState(BottomSheetBehavior.STATE_COLLAPSED);         }     });     offer_info_dialog.setOnDismissListener(new DialogInterface.OnDismissListener() {         @Override         public void onDismiss(DialogInterface dialog) {             rel.setVisibility(View.VISIBLE);         }     });  }   and this is an error:  java.lang.NullPointerException: Attempt to invoke virtual method 'android.view.View android.support.design.widget.BottomSheetDialog.findViewById(int)' on a null object reference

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've searched for this question in vain. Does anyone know why the Fn key can't be assigned? The OS accepts all keys(even the keys that are set as shortcut by default, can be changed). What makes  the Fn key  different from other keys?  Is there a way to change this behavior and use it for shortcuts?

I like to know how Fn keys work in my laptop. I think a kernel module exist that catch Fn key and call some scripts to do something. In my laptop, Fn+F2 switch power of wireless and blue-tooth.   this is output of acpi_listen, when i press Fn+F2  hotkey ATKD 0000005d 00000019 hotkey ATKD 0000007e 00000009   and, folloing is output of xev for Fn+F2  keycode 238 press keycode 238 release keycode 237 press keycode 237 release   I guess whenever i pressed Fn+F2 two events are jumped out. I tried to find what actions are executed for this keys. any idea appreciated ;)


I want to check the results of a restore from backup. This is, because TimeMachine on MacOS gives me some weird errors and warnings and I want to make sure, everything is in its place again after restoration. While I don't trust TimeMachine to put every file back, I trust it to put every file it restores with the correct content.   I thought about diff -r, but going through roughly 300 GiB may take eternally. I'm fine to compare at least the presence of files but comparing size and date in the same run is even better.   I'm aware of solutions like  diff <(ls -R $PATH1) <(ls -R $PATH2)   but the output is diffish to read. I'd rather like a single line per file found on only one side. Also I have to rely on ls proceeding through the tree in the same order on both sides. This may be different because filesystems may differ.   I'd love most to get a tool for the lazy which takes two pathes and outputs differences up to any desired level of inspection, perhaps something out of macports. But I don't fear ample bashisms.

With diff -r  I can do this task, however it takes so long because diff checks file's content. I want something that determine that two files are the same regarding of their size, last modified, etc. But no checking bit by bit the file (for example a video takes sooo long). Is there any other way?


$$ y_t = θy_{t−1} + u_t \\ t = 1,...,T;  $$ I need to derive a formula for $y_t$ and show that  $$ E\left[\frac{\Sigma y_{t-1}u_t}{ \Sigma(y_{t-1})^2}\right] \neq 0 $$

I am having trouble understanding the estimation of an AR process. In some textbooks, the AR(1) process is defined as follows: $y_{t}=\theta y_{t-1}+ϵ_t$ (which does not contain a constant). So the OLS estimator is biased. I am confused about the cause of the bias. It is explained that $y_{t-1}$ is dependent on $ϵ_{t-1}$ although it is independent of $ϵ_t$. However in linear regression, if the equation does not contain a constant, we cannot make sure the expectation of disturbance is zero. So the OLS estimator is bias without a constant. Does it mean that the OLS estimator is unbiased if I add a constant in AR process?


Haven't found anything about the issue I'm experiencing and would like someone to help me with it. I'm trying to install Ubuntu 14.04, but for some reason installation does load, but I get on monitor tiles of size 4px by 8px in zig-zag black/orange and can't see anything from them.   Managed somehow to get to select screen, but that is where issues start since I can't discern what option is what.  Anyone has idea how to fix it?  See screenshot below:

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


Prove for any positive number $t$, there is a solution for $x^2=t$.  So we want to show that $x^2=t$ for $t\geq0$.  We can break this into two cases:  Case 1: Assume $t=0$, then we have $x^2=0$ $\Rightarrow$ $x=0$, and we are done.  Case 2: Assume $t>0$, then we have $x^2=t$ $\Rightarrow$ $x=\sqrt{t}$  And here is where I'm stuck, not sure what I should do next...?

I am self-studying real analysis for fun and came across the following question (from A First Course in Real Analysis by Berberian).  (i) Prove the following: If $r$ is a real number such that $0 \leq r \leq 1$, then there exists a unique real number $s$ such that $0 \leq s \leq 1$ and $s^2 = r$. (ii) Generalize (i) to the following: If $a \in \mathbb{R}$, $a \geq 0$, then there exists a unique $b \in \mathbb{R}$, $b \geq 0$ such that $b^2 = a$.  Put $y = 1-r$ and $x = 1-s$. Then we want to find a real number $x \in [0,1]$ such that $(1-x)^2 = 1-y$. I am trying to find an increasing sequence $(x_n)$ such that $0 \leq x_n \leq 1$ (defined recursively). For (ii) how could I use (i) to get the result?


since we know that gravitational force is nothing but a curvature in space-time. I have a similar analogous for the electric or magnetic charges. Similarity is that both electromagnetic and gravitational forces follow the inverse square law. consequence of this can be that we can have a another interpretation of electron orbital motion causes by curvature in space due to electric charge (as mass of electron is very small so STR have no significance here). But problem is that we have two different type of charges (+ve and -ve) which gives repulsion and attraction, whereas in gravitation force mass always gives the attraction forces. Please correct me if I am wrong.

I apologize if this seems like a quack question, but I need some insights by those who know much more than me in Physics.  Anyway, the gravitational "force" (not really a force) is a manifestation of the curvature of space-time, caused due to presence of mass. Suppose I conjecture that ANY force (electroweak, strong...) is also a manifestation of some property of space-time effected by "something" (as in mass in the case of gravity, and different for different types of forces).  So is there any blatant fault with this line of thought? (I'm asking for blatant faults, since it's a wild supposition anyway)


We have: $$ x^{x^{x^{ x^{x ^{x ^{\dots}}}}}} =  2.$$   I tried a reasoning by recursion:  For $n=1$: \begin{align}  x^x &= 2 \\ \implies x\ln x &= \ln 2 \end{align}  For $n=2$: \begin{align}  x^{x^x} &= 2 \\ \implies x\ln x^x &= \ln 2  \\ \implies x^2\ln x  &= \ln 2 \\ \end{align}  For an arbitrary $n$ we can solve: $$x^n \ln x = \ln 2 $$  But for $n \to \infty$, I can't seem to find something. Does anyone have an idea on how to tackle this problem?

I came up with this little simple exercise, stating:  $x^{x^{x^{\dots}}}$ infinite times is equal to $2$, find $x$.   As we're dealing with infinity, we can just separate the first $x$ and get $x^2=2 \implies x=\sqrt2$  But then I thought what if we change $2$ to $4$? Now we get $x^4=4 \implies x=\sqrt[4]4=\sqrt2$  Something went wrong, can someone explain?


I have the below query where I am trying to arrange the "weekNumber" in ascending order such as week1,week2,week3,week4,... and so on  SELECT WeekNumber,pointsRewarded FROM chart_copy  WHERE EmployeeID = '2164' order by WeekNumber asc ;   But the problem is it is not giving me the desired output.  What it gives is this :    Kindly help.I am using sql server -2012.

We have a large database on which we have DB side pagination. This is quick, returning a page of 50 rows from millions of records in a small fraction of a second.  Users can define their own sort, basically choosing what column to sort by.  Columns are dynamic - some have numeric values, some dates and some text.  While most sort as expected text sorts in a dumb way. Well, I say dumb, it makes sense to computers, but frustrates users.  For instance, sorting by a string record id gives something like:  rec1 rec10 rec14 rec2 rec20 rec3 rec4   ...and so on.  I want this to take account of the number, so:  rec1 rec2 rec3 rec4 rec10 rec14 rec20   I can't control the input (otherwise I'd just format in leading 000s) and I can't rely on a single format - some are things like "{alpha code}-{dept code}-{rec id}".  I know a few ways to do this in C#, but can't pull down all the records to sort them, as that would be to slow.  Does anyone know a way to quickly apply a natural sort in Sql server?    We're using:  ROW_NUMBER() over (order by {field name} asc)   And then we're paging by that.  We can add triggers, although we wouldn't. All their input is parametrised and the like, but I can't change the format - if they put in "rec2" and "rec10" they expect them to be returned just like that, and in natural order.    We have valid user input that follows different formats for different clients.  One might go rec1, rec2, rec3, ... rec100, rec101  While another might go: grp1rec1, grp1rec2, ... grp20rec300, grp20rec301  When I say we can't control the input I mean that we can't force users to change these standards - they have a value like grp1rec1 and I can't reformat it as grp01rec001, as that would be changing something used for lookups and linking to external systems.  These formats vary a lot, but are often mixtures of letters and numbers.  Sorting these in C# is easy - just break it up into { "grp", 20, "rec", 301 } and then compare sequence values in turn.  However there may be millions of records and the data is paged, I need the sort to be done on the SQL server.  SQL server sorts by value, not comparison - in C# I can split the values out to compare, but in SQL I need some logic that (very quickly) gets a single value that consistently sorts.  @moebius - your answer might work, but it does feel like an ugly compromise to add a sort-key for all these text values.


Show that $n$ divides $\phi(a^n -1)$ for any $a>n$ where $\phi$ is Euler's totient function.  I would really appreciate a hint.

Let $n$ and $a$ be positive integers with $a > 1$. I need to show that $n$ divides $\phi(a^n -1)$.   Here, $\phi$ denotes the .  Could any one give me a hint?


There is a difference in the difficulty by which the two different objects can be lifted up.   Is "by" correct here? Does "difficulty by which" sound natural? is there maybe a better alternative?  Thanks a lot in advance!

I have come across the phrases like "to which","for which", "by which", "on which" and so on(using a preposition with a relative pronoun).   e.g. The chair on which the body was found..  Could someone please explain if there's a particular rule to be followed when building/using them?   Can I use any preposition before 'which'?  What if I say "The chair which the body was found on"? How would I decide which preposition to be put? Can I use other relative pronouns too?  Thanks in advance.


I don't have access to an oven but I do have access to a cast iron pot and an induction stove. Is it possible to bake bread and make pizza etc with this setup with a little experimentation?

How can I bake a pizza without an oven (or any other fancy stuff, so no suggesting of charcoal, sun oven, and so on).  Just using a plain heating element on the bottom, like a burner, what are the alternatives? What is better than a pizza on the frying pan?  Can I put a pizza stone on a burner, or would the direct heat crack it?


I have GPS locations with date. These are points.  I want to convert the points to lines, sorted by date.  Using PostgreSQL  Tried:  SELECT observations.id,        ST_MakeLine(observations.geom ORDER BY observations.date) AS newgeom FROM   observations  GROUP BY        observations.id ;   The problem is that the single line values gives the same coordinates. So, there will be no line. 0 and 1 are the same.    How is this possible?

How do i create a linestring from points sort by date in PostgreSQL?  I tried:  SELECT observations.id,    ST_MakeLine(observations.geom ORDER BY observations.date) AS newgeom    FROM   observations     GROUP BY    observations.id;   This is going wrong. It returns me a linestring with same coordinates.  So, instead of a line from a to b, it gives me a to a.    What am I doing wrong?


My question is: When is $\sum_{i=1}^n i$ a square number?  I know that this means i have to solve $n(n+1)/2=m^2$. I tried with modulo 2 etc. but i don't get to it. Please help.

Prove there is an infinite amount of natural numbers for which $\displaystyle \frac{n(n+1)}{2}$ is a perfect square.


If two continuous random variables have exactly the same expected value and variance, do they always have the same distribution?

Are there any non-identical distributions which happen to have the same moment-generating function?


When using gedit , i always need to edit file in /etc/ or /usr/ which need to be root. So i created a Launcher shortcut on the left with command sudo gedit.  So every time i click the icon on the left Launcher, gedit will started as root. But the problem is that, when i modified other files, such as files in /home, the owner of file will also be changed to root. I don't want to do this, i just want to save this file without modifying its owner, and i don't want to bother every time to restart gedit as root to modify files owned by root. How to do it?

I've read  and am interested in this line:     You should never use normal sudo to start graphical applications as Root.   Why? What is the difference? Please provide a simple explanation, as I'm just a normal desktop user.


Can $\int_0^1 f^2(x)dx<\infty$ imply $\int_0^1 |f(x)|dx<\infty$, if $f$ unbounded near $0$.    The converse is wrong, since $f(x)=1/\sqrt{x}$ is an example.

Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?   So I know that $| \int_0^1 g(x)dx | \leq \int_0^1 |g(x)|dx = \int_0^1 \sqrt{g^2(x)}dx$. Not sure how to continue.


Let $$ f:X\rightarrow Y $$  If $f$ is defined on $X$ such that every compact set in $X$ is mapped to a compact set in $Y$. Is $f$ a continuous map?

A continuous function maps a compact set to a compact set. Is the converse of this true? That is, is a function that maps every compact set to a compact set necessarily continuous?


Example on :  No problem on other SE websites where I am not suspended.

While any of the other sections under "Edit Profile & Settings" do work normally.


Is there any penalty for building a new city "far away" from your other cities?  That is, if I remember correctly from Civ4, (city) maintenance was higher if a new city was "far away" from my current empire. Is this (still?) true in Civilization 5?

In Civ 4 there was a serious penalty when you settled a city far away from your main capital.   What is the position on this in Civ 5? Should I scatter shot my cities far away? Or place them close to my capital?


I was trying to solve the following question. For a positive real number x, prove that $$[x]+\frac{[2x]}{2}+\frac{[3x]}{3}+\cdots+\frac{[nx]}{n}\leq [nx]$$where [] represent the Greatest Integer Function.  Here is my approach. I used Hermite's Identity to reduce $[nx]$ to $[x]+[x+\frac{1}{n}]+[x+\frac{2}{n}]+\cdots+[x+\frac{n-1}{n}]$ and came across the following lemma.   Lemma: For positive real x and $k=1,2,\cdots,n$, prove that $$\left[x+\frac{k-1}{n}\right]\geq \frac{[kx]}{k}$$which solves the question directly  Could anyone please verify this equation. If true, please provide a proof for it as well. I tried using induction but fell short  Thanks a lot for the help!!:)

Is true that $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]$, for every $x\in\mathbb{R}$ and for every $n\in\mathbb{Z}^+$?  My work:  Let $x\in\mathbb{R}$ be given. For every $k=1,\dots,n$, define $i_k\in\{0,1,\dots,k-1\}$ such that  $$ [x]+\frac{i_k}{k}\leq x<[x]+\frac{i_k+1}{k}\hspace{20mm} (*). $$  On one hand, we have that $[kx]=k[x]+i_k$ for every $k=1,\dots,n$.  So  $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}=n[x]+\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}=[nx]+\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}-i_n$  Thus  $$\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]\Leftrightarrow\displaystyle\sum_{k=1}^n\dfrac{i_k}{k}\leq i_n\,.$$  On the other hand, from $(*)$ is direct that $i_k=[k(x-[x])]$. Thus  $$\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]\Leftrightarrow\displaystyle\sum_{k=1}^n\dfrac{[k(x-[x])]}{k}\leq [n(x-[x])]\,.$$  In other words, we can assume that $x\in[0,1)$.   Now the questions is:  Is true that $\displaystyle\sum_{k=1}^n\dfrac{[kx]}{k}\leq[nx]$, for every $x\in[0,1)$ and for every $n\in\mathbb{Z}^+$?  Any simpler approach? Any thoughts?


I integrated $\dfrac{\log x}{1+x^2}$ from $0$ to infinity with residue calculus and got... $0$.  This also agrees with Wolfram Alpha.  How can this be?    Is it due to the behavior of $\log(x)$ near the origin?  Like a cancellation effect?    Thanks,

Find $\displaystyle \int_{0}^{\infty} \dfrac{\ln(x)}{1+x^2}dx$.   How should I change the limits of integration to evaluate this?


I am trying to understand convergence in Lp spaces a little bit better.  If we have $p, q \in [1, \infty]$ and a sequence of functions $(f_n)_{n\in\mathbb{N}} \subset L^p(\mathbb{R}^d) \;\cap\; L^q(\mathbb{R}^d)$ with   $\Vert f_n - f \Vert_p \rightarrow 0$ for some $f \in L^p$ and $\Vert f_n - g \Vert_q \rightarrow 0$ for some $g \in L^q$.   Is it then true that $f = g$ almost everywhere?  I can't think of a good counter example or a proof.

If I have a sequence $\{f_n\}_{n\in \mathbb{N}} \subset L_p\cap L_q$ that is Cauchy under both norms,  I am wondering if $f_n \to f$ in $L_p$ implies that $f_n\to f$ in $L_q$.   I have been working on this but I can't seem to figure out a definite proof.  Thank you!  PS: $1\leq p<q <\infty$


Is it possible to construct a scope like this  User.where(:id => [5,4,3,2,7,1000] )   in a way, that  a) the results are in the order of the ids passed. (This is the simple part, since you can just load the records, and sort the result accordingly)  b) the result is not an array but a scope in itself (The tricky part ;)  Update: Solutions that only work on MySQL are welcome.

I am wondering if there is away (possibly a better way) to order by the order of the values in an IN() clause.  The problem is that I have 2 queries, one that gets all of the IDs and the second that retrieves all the information. The first creates the order of the IDs which I want the second to order by. The IDs are put in an IN() clause in the correct order.  So it'd be something like (extremely simplified):  SELECT id FROM table1 WHERE ... ORDER BY display_order, name  SELECT name, description, ... WHERE id IN ([id's from first])   The issue is that the second query does not return the results in the same order that the IDs are put into the IN() clause.  One solution I have found is to put all of the IDs into a temp table with an auto incrementing field which is then joined into the second query.  Is there a better option?  Note: As the first query is run "by the user" and the second is run in a background process, there is no way to combine the 2 into 1 query using sub queries.  I am using MySQL, but I'm thinking it might be useful to have it noted what options there are for other DBs as well.


I want to apply to a doctoral program in mathematics (I am currently a master's student) that is strong in algebra. The schools I found that have what I am interested in are "tier 1" schools with very competitive admissions and I am not sure what to do to improve my application. I had to withdraw a semester after my first year of graduate school because of several health problems, and when I went to the doctor I was told I had severe iron deficiency anemia as well as another medical issue I do not want to discuss here. I had it for almost ten years, but my previous doctor never diagnosed it. My GPA has suffered a lot from its side effects (it is 3.3) and also my subject GRE from undergrad is terrible (560). I was not able to retake the subject GRE because of a time conflict.  I want to apply for Fall 2016 because my health is a lot better now, but I am not sure what to do to make my application better. I feel like if I try to explain my health issue it will look like I am trying to make excuses. I have done seminar presentations, gone to an algebra conference, and done independent work without a faculty adviser (they always seem to tell me they are too busy or that I should stop studying material outside of classwork).  If someone can offer a suggestion on how I should approach explaining my situation or could suggest something for me to do to make myself more competitive, it would really help.

When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.


today I just upgrade my ubuntu 12.04 to 14.04.  The problem is that I cannot play local swf files.  Even after installing flash player you cannot play swf files.   I can play online flash games in browser but not swf files when you have them downloaded in your computer  Any fix for this problem?  I tried gnash but that won't open swf in browser so the data that I have saved in cookies for that specific swf file won't restore.  This problem is same for all browsers I have tried. (chrome, chromium, firefox)  what I have tried is this command:    sudo update-pepperflashplugin-nonfree --install and this one:    sudo apt-get install flashplugin-nonfree-extrasound  just installed flash plugin for chrome still not fixed this is what I did: downloaded a tar file from adobe then these 3  commands:  sudo mkdir /opt/google/chrome/plugins sudo cp libflashplayer.so /opt/google/chrome/plugins sudo cp –r usr/* /usr   the internal flash player for chromium is activated:   and also I tried gnash which didn't open my file. you can download the swf file from this site:       there is a free version  Temporary solution for this problem is to upload your swf file to a website (then you can view it from browser). I use

Does anyone know what libraries I have to install to play .swf files?


An enemy hit by Hypnotic Pattern is charmed (0 speed and incapacitated).  Does this make any sort of non-damage saves such as dex saving throw fail automatically because enemy is charmed / 0 speed / incapacitated?

I'm reading the Hypnotic Pattern description and it says "Charmed, Incapacitated, Speed (0)" and "Snaps out of it, if being shaken or takes damage."  Then I read the various states you can be under:     Charmed: can't attack the caster   Incapacitated: can't take actions or reactions - is a save an action/reaction?   Immobilized (Speed 0): Somewhere between Paralyzed, Restrained and Stunned — which all say you auto fail Strength and Dexterity saves and people have advantage on attacking you.   If I were to Fireball an individual (or group) under the influence of Hypnotic Pattern, would they get a Dexterity save to duck out of harm's way?


For observers, this particular badge creates confusion. Currently Electorate badge text shows like this:     Vote on 600 questions and 25% or more of total votes are on questions.   Does it mean:      Vote on 600 posts and/or 25% or more of total votes are on questions.   ... or something better. To me clearly, the original text is not understandable. The "and" part appearing between a number (600) and % (25) is creating confusion.  Update: From the dupe, I learned that the badge is intended the way it is. However below problems are still open:   Is this any vote or just upvote? Should it be "AND" or "OR"?   Practical example: When a user upvotes 600 Qs, then he is surely eligible for the badge. Now, A user votes up 1000th post. This is also the 600th Q. Hence 60%. Is the user eligible for the badge?  Should the text be corrected?  Suggestion:     Vote on 600 questions, which is at least 25% of total votes

There is a badge named Electorate which is going to be awarded on "Voted on 600 questions and 25% or more of total votes are on questions". Can somebody explain this to me?  Voted on 600 Question and 25% are on Question? is this  means   Voted on 600 Posts and 25% are on Question  Can't SO place some easy text or Definitions for average users?


ls / outputs two lines.  $ ls /  bin   cdrom  etc   initrd.img      lib    lost+found  mnt  proc  run   share  sys  usr  vmlinuz boot  dev    home  initrd.img.old  lib64  media       opt  root  sbin  srv    tmp  var  vmlinuz.old   But why does ls / | wc -l tell 26 lines?  $ ls / | wc -l 26

I think I may be overlooking a relatively fundamental point regarding shell. Output from the ls command by default separates output with newlines, but the shell displays the output on a single line.  Can anyone explain this to me? I had always presumed that the output was simply separated by spaces, but now that I see the output separated by newlines, I would expect the output to be displaying on separate lines.  Example:  cpoweradm@debian:~/lpi103-4$ ls text* text1  text2  text3   od shows that the output is separated by newlines:  cpoweradm@debian:~/lpi103-4$ ls text* | od -c 0000000   t   e   x   t   1  \n   t   e   x   t   2  \n   t   e   x   t 0000020   3  \n 0000022   If newlines are present, then why doesn't the output display as:  text1  text2 text3


trying to start deluge daemon (deluged) on Ubuntu 15.10 but I'm getting this error on the status:  chris@fileserver:~$ systemctl status deluged ● deluged.service - Deluge Bittorrent Client Daemon    Loaded: loaded (/etc/systemd/system/deluged.service; enabled; vendor preset: enabled)    Active: failed (Result: start-limit) since Mon 2015-10-26 09:52:26 EDT; 51min ago   Process: 1340 ExecStart=/usr/bin/deluged -d (code=exited, status=1/FAILURE)  Main PID: 1340 (code=exited, status=1/FAILURE) Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Unit entered failed state. Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Failed with result 'exit-code'. Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Service hold-off time over, scheduling restart. Oct 26 09:52:26 fileserver systemd[1]: Stopped Deluge Bittorrent Client Daemon. Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Start request repeated too quickly. Oct 26 09:52:26 fileserver systemd[1]: Failed to start Deluge Bittorrent Client Daemon. Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Unit entered failed state. Oct 26 09:52:26 fileserver systemd[1]: deluged.service: Failed with result 'start-limit'.

Can someone help me get deluged running on 15.10?  Every how-to I can find is for init.d not systemd.  The deluged package installs no startup scripts for either init.d (which would work in compatibility mode) or systemd. So what do you need to do to get systemd to start deluged?


I wanted to understand how to solve these types of questions in Combinatorics in which there is a recurrence relation. For example, this question states:  Consider a binary string which consists only of digits 0 and 1, let an be the number of such strings with $n$ digits such that 11 doesn't come anywhere in the string. Find the relation between $a_n, a_{n-1}$ and $a_{n-2}$.  Now I have no idea how to solve this question, any help or solution would be much appreciated.

Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s.  I know my base case:$$a_1 = 2$$ for either $1$ or $0$. Normally to construct the recurrent relation I would say fill in $n-1$ spaces then add a $1$ or $0$, which is simply:$$a_n = 2\cdot a_{n-1}$$However, I don't believe this is right, because this doesn't take into account that there can't be any consecutive $1$s.  Even when I use the base case of $2$ digits:$$a_2 = 3$$for either $01$, $10$, or $00$, I still get the recurrence relation of:$$a_n = 3\cdot a_{n-2}$$which also does not account for $01$ and $10$ occurring consecutively.   So how would I express this?


With Christmas around the corner, I'd like to make my system's prompt (for every user) a bit more festive and cheery.  Namely, I'd like to attach a Happy Holidays! (or similar) message post-login for every user on the system (on terminal login, SSH or locally). I'd assume this is a simple echo command, but I'm not sure where the appropriate place to put this command is in such a way that it would affect everyone. For obvious reasons, I'd rather not modify everyone's .bashrc. So, where is that?

I want my shell prompt to look like a cheeseburger! 🍔🍔🍔  It would be nice if it also displayed: username, hostname, and current directory.


We know that a Boggart exists even if nobody sees it:  Nobody knows what a Boggart looks like if nobody is there to see it, although it continues to exist, usually giving evidence of its presence by rattling, shaking or scratching the object in which it is hiding.    Now, I can, for example, imagine a situation of an older brother telling horrible stories from Hogwarts to his little brother to scare him. It could also include a story about this really scary class where the Boggart is taught. This creature which transforms to your biggest fears. The story would make the little one so scared of a boggart that it would become his biggest fear despite the fact that he didn't ever saw it. Would his boggart have its natural form? I don't need to know how the natural form of a boggart looks, but if this is an in-universe way to find it out.

Rereading the Prisoner of Azkaban, this interesting question(at least to me) popped in my head. What shape would a boggart take if a person is never depressed about anything, has no evil memories whatsoever for the boggart to feed on or has no fear?


I was wondering: What is the origin of asking someone to say "when" (to mean "enough") while they are serving food or beverages?

When a waiter at a restaurant comes by with pepper or Parmesan cheese, he says, "say when" and starts putting it on your food.  Many people will say "OK" or "that's enough," but it seems that the customary answer is "when".  How did this become the customary answer?  Did everyone decide to make the exact same joke, until it became commonplace.  I thought it was funny when I was a kid, but even now as an adult, I still say it.  For evidence that this is indeed commonplace, see .  The answer "when" is used and is external to the joke of the strip. But even so, I'm curious as to just how commonplace this really is.  I see it a lot in the US.  Is it used elsewhere in the world?  (by the way, I'm new to asking questions on this site, and I have no idea what tags to put on this question)


It is known that Axiom of Choice implies the following statement:     For each two sets $A$ and $B$, there is a one to one function from $A$ to $B$ iff there is a function from $B$ onto $A$   Is above statement an equivalent form of Axiom of Choice or it is strictly weaker?

Given a family of sets $(A_i : i \in I)$, we define the disjoint union: $$\sum_{i \in I} A_i = \bigcup_{i \in I} (\{i\} \times A_i).$$  There is a surjection $\sum_{i \in I}A_i \to \bigcup_{i \in I} A_i$ given by $(i,a) \mapsto a$, so by the Axiom of Choice there is an injection $\bigcup_{i \in I} A_i \to \sum_{i \in I}A_i$.  My question is whether AC (or some fragment of it) is required to prove that there is an injection $\bigcup_{i \in I} A_i \to \sum_{i \in I}A_i$.  (If I remember correctly, it is not known whether "every surjective image of any set $X$ injects into $X$" implies AC.)


09:00.0 Network controller: Ralink corp. RT3290 Wireless 802.11n 1T/1R PCIe  Output of command ifconfig:    Output of command sudo lshw -C network:    How can I make my WiFi connections stable and stop them from disconnecting automatically?  Everyone who said it is a duplicate of some other questions , those solution didn't fix my problem :( . Please help

I just installed Ubuntu 12.10 on an ASUS X401U, and after installation there is no list of wireless connections. I didn't have that problem with an installation on HP. What I can do to enable Wifi?  07:00.0 Network controller [0280]: Ralink corp. Device [1814:3290]


I am a International Student studying in London with a Tier 4 Student VISA. Am I eligible to invest in stocks, bonds or funds through brokers or banks in the United Kingdom?  I tried to search Home Ministry documents for information, but I can't seem to find useful information.

Can holders of a "Tier 2 Skill Transfer UK Visa" invest in the London stock market?  If so, what is the procedure?


I got my new lg g3 and when i try to download something it says that there is insufficient space on the device. I looked up some solutions and google play services doesn't let me uninstall updates. are there other solutions? Btw i have about 8 gb of storage left

Every time I go to install a new app, I get the message "Insufficient storage", and an unable to install anything!  I am using Samsung GT19060 my internal memory is 8GB. I have not downloaded anything but anytime I try to download something it will tell me low memory space.


I'm now making commercial software for Windows CE O/S, and I want to embed Ubuntu font to my software. The file format will be converted to my own format to speed up my software.  In this case, am I need to obtain some kind of license? Or do it freely with including license.txt files on my software ?

Huge Ubuntu fan here, I really like the Ubuntu font, but as far as I know you may only use it in open-source applications. I want to use it in an iPhone/iPad app. Due to Apple's contracts, I can't make the project open-source.  So, the question actually is, is it allowed to use/distribute the Ubuntu font in an iPhone/iPad application (free or paid)? Would be great if that's allowed!


My hosting service company said your site got pishing attack public_html/.well-known/acme-challenge/index.php' Known exploit = [Fingerprint Match] [PHP Obfuscated Include Exploit [P1693]] My concerned is, what to be filled in that and what to be removed, help me plz i will thankful to you I want help on my

This is a  about Server Security - Responding to Breach Events (Hacking)   See Also:                  Canonical Version I suspect that one or more of my servers is compromised by a hacker, virus, or other mechanism:   What are my first steps? When I arrive on site should I disconnect the server, preserve "evidence", are there other initial considerations? How do I go about getting services back online? How do I prevent the same thing from happening immediately again? Are there best practices or methodologies for learning from this incident? If I wanted to put a Incident Response Plan together, where would I start? Should this be part of my Disaster Recovery or Business Continuity Planning?   Original Version       2011.01.02 - I'm on my way into work at 9.30 p.m. on a Sunday because our server has been compromised somehow and was resulting in a    attack on our provider. The servers access to the Internet   has been shut down which means over 5-600 of our clients sites are now   down. Now this could be an FTP hack, or some weakness in code   somewhere. I'm not sure till I get there.      How can I track this down quickly? We're in for a whole lot of   litigation if I don't get the server back up ASAP. Any help is   appreciated. We are running Open SUSE 11.0.            2011.01.03 - Thanks to everyone for your help. Luckily I WASN'T the only person responsible for this server, just the nearest. We managed   to resolve this problem, although it may not apply to many others in a   different situation. I'll detail what we did.      We unplugged the server from the net. It was performing (attempting to   perform) a Denial Of Service attack on another server in Indonesia,   and the guilty party was also based there.      We firstly tried to identify where on the server this was coming from,   considering we have over 500 sites on the server, we expected to be   moonlighting for some time. However, with SSH access still, we ran a   command to find all files edited or created in the time the attacks   started. Luckily, the offending file was created over the winter   holidays which meant that not many other files were created on the   server at that time.      We were then able to identify the offending file which was inside the   uploaded images folder within a  website.      After a short cigarette break we concluded that, due to the files   location, it must have been uploaded via a file upload facility that   was inadequetly secured. After some googling, we found that there was   a security vulnerability that allowed files to be uploaded, within the   ZenCart admin panel, for a picture for a record company. (The section   that it never really even used), posting this form just uploaded any   file, it did not check the extension of the file, and didn't even   check to see if the user was logged in.      This meant that any files could be uploaded, including a PHP file for   the attack. We secured the vulnerability with ZenCart on the infected   site, and removed the offending files.      The job was done, and I was home for 2 a.m.            The Moral   - Always apply security patches for ZenCart, or any other CMS system for that matter. As when security updates are released, the whole   world is made aware of the vulnerability.   - Always do backups, and backup your backups.   - Employ or arrange for someone that will be there in times like these. To prevent anyone from relying on a panicy post on Server   Fault.


If I have an older PC laptop, that doesn't have 2g of harddrive space, which older version should I use?

For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements?


To index a nontrivial TeX expression expr, we use the command \index{str@expr}, where str is a simplified (typically plain ASCII) representation of expr to be used for sorting.  However, str@expr is parsed incorrectly inside a footnote:  \documentclass{report} \usepackage{imakeidx} \makeindex  \def\gnu{\texttt{Gnu}} \def\gnat{\texttt{Gnat}} \begin{document} Some text\index{Gnu@\gnu}\index{Gnat@\gnat}.  \pagebreak Some more text\index{Gnu@\gnu}.\footnote {A footnote.\index{Gnat@\gnat}}  \printindex \end{document}   This generates the following .idx file  \indexentry{Gnu@\gnu}{1} \indexentry{Gnat@\gnat}{1} \indexentry{Gnu@\gnu}{2} \indexentry{Gnat@\texttt  {Gnat}}{2}   The two index entries for 'Gnat' differ, and therefore \Gnat appears twice in the index, as shown in this screenshot:    How does \footnote modify the \index command, and what can be done about it?

In document class book, and package caption, creating index with makeidx. Index entries for the main text and for footnotes collate properly; but those for captions create their own entries.  Example: for the tag \index{New York!Custom House!\textit{Cartouche}}, text and footnotes collate properly; but used in a caption, a new entry is created at the third level, and is also out-of-alphabetic-sequence. Note: the top level, and first sub are correct; only the second sub is duplicated.  How to get the caption index entries under the same entry?


I used the \setlength\parindent{12pt} to try to add indent at the beginning of every paragraphs. But it only works for very few paragraphs (7 paragraphs in chapter 1 only 1 paragraph got indented.).  Since I am using a Latex template of the thesis from my school. I cannot give an example of my problem here. Could anyone please give me some suggestion what may cause this kind of problem?  I got no errors but 4 warnings and 92 bad boxes after when I tried to create the pdf. But everything in the pdf looks fine( different tables, plots, bullet points all looks fine) except the indent.  It seems like latex cannot detect the paragraphs correctly. (I use \\ to separate paragraphs) Because I also tried to set \parskip to a particular value, it only works for adding space between chapter/section names and paragraphs, didn't add space between paragraphs, either.

What is the difference between \par, \newline, \\ and blank lines? When should I use which one?


I'm not sure if this is an acceptable place to ask this question, as it may have more to do with the biological workings of human eyes than with the physical properties of light, but I'd rather hear a physical explanation than a biological one (if one exists).   Essentially, we often describe the visible spectrum with a color wheel. In this wheel, Red appears next to Purple (violet), but Red and Violet are at opposite ends of the visible light spectrum. What accounts for this? That is, why do we perceive the Visible Light Spectrum as circular, instead of linear?

When people are asked to match monchromatic violet light with an additive mix of basic colours, they (paradoxically) mix in red.  In fact, the CIE 1931 color space chromaticity diagram shows this effect begins at about 510nm (greenish-cyan), where people mix in no red.  From that point on, the higher the frequency of the light source, the more red they mix in.    This effect is reflected by the red curve of the , which has an additional bump in the area of blue light.  However, that curve does not match the actual spectral sensitivity of red cones.  So where does this additional perception of red at higher frequencies come from?


I would like to bind multiple CheckBox items (IsChecked property) to a single property in my ViewModel.    The ViewModel property is called SelectedWeekdays (int) and is the sum of all the selected weekdays. The idea being that every possible combination of weekday values will always result in a unique sum. The weekdays are defined in an enum as such:  public enum Weekdays {     Monday = 1     Tuesday = 2     Wednesday = 4     Thursday = 8     Friday = 16     Saturday = 32     Sunday = 64 }   So for example if Tuesday and Thursday are selected on the View, this should result in a ViewModel property value of 10.  Likewise, if the ViewModel property changes, say to 3, the CheckBoxes for Monday and Tuesday should be checked.  I've looked at MultiBindings but it seems I could only use that to bind a single CheckBox to multiple values. Can you point me in the right direction?

I've got an enum like this:  public enum MyLovelyEnum {     FirstSelection,     TheOtherSelection,     YetAnotherOne };   I got a property in my DataContext:  public MyLovelyEnum VeryLovelyEnum { get; set; }   And I got three RadioButtons in my WPF client.  <RadioButton Margin="3">First Selection</RadioButton> <RadioButton Margin="3">The Other Selection</RadioButton> <RadioButton Margin="3">Yet Another one</RadioButton>   Now how do I bind the RadioButtons to the property for a proper two-way binding?


I am trying to calculate the following limit, but to be honest I've been failing miserably.  $\lim\limits_{n\rightarrow\infty}\frac{\sqrt{1+\frac{1}{n}}+\sqrt{1+\frac{2}{n}}+...+\sqrt{1+\frac{n}{n}}}{n}$  I've been trying to use the fact below but got me no useful result:  $\sqrt{a+b}\leq\sqrt{a}+\sqrt{b}$  Also I've been trying to use the logarithm to obtain a product but still no results.  Any hints, please?  Update 1:  I followed your advice and identified the function $f(x)=\sqrt{1+x}, f:[0,1]$  So I guess now the result of that limit is $\int_0^1{\sqrt{1+x}}$ ?

Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$  What method to use in order to find the closed form of summation $\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}$?


I came across some sentences and I was wondering which word is correct: 'train,' 'to train' or 'training'?  What we should do is train our workers to become more efficient.  All I we do is train our workers...  All you have to do is train workers...

I was speaking to an English learner and said, “All you have to do is read a lot.” And they thought that sentence wasn’t grammatically correct because I dropped the word to between is and read.  They thought it should be “All you have to do is to read a lot.” That sounds weird to me.   How do I explain to them the reason you drop the to? Or am I incorrect and it really should have a to?


While playing around with Amazon EC2, I noticed that the Ubuntu images showed available updates at login (See pic)  How can I get my home installation to do this? I'm running 14.04.    My question is specifically in reference to packages/security updates. In the image, they are represented as "0 packages can be updated." and "0 updates are security updates." All other information showed up without the fix that I referenced as a comment to the duplication flag. I've discovered two solutions for the problem:   Running tasksel allows the selection of the Basic Ubuntu server collection An abbreviated form of tasksel appears at the end of a fresh installation, which also allows the selection of Basic Ubuntu server

Is there a way to get the fancy MOTD that shows up on an Ubuntu Server install on my Ubuntu Alternate install? Like this:  Welcome to Ubuntu 11.10 (GNU/Linux 3.0.0-12-server x86_64)   * Documentation:  https://help.ubuntu.com/11.10/serverguide/C    System information as of Sun Nov  6 00:38:01 PDT 2011    System load:  0.0                Processes:           88   Usage of /:   0.8% of 227.98GB   Users logged in:     0   Memory usage: 14%                IP address for eth0: 10.13.37.147   Swap usage:   0%    Graph this data and manage this system at https://landscape.canonical.com/


I found this question while browsing through "The Probabilistic Method", by Noga Elon.  Let X and Y be 2 independent and identically distributed real valued random variables. Prove that: $$P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$$  So I tried the following:  $$P\{|X-Y| \leq 2\} = P\{|X-Y| \leq 1\} + P\{X-Y \in (1,2]\cup[-2,-1)\}$$ $$= P\{|X-Y| \leq 1\} + P\{X-Y \in (1,2]\} + P\{X-Y \in [-2,-1)\}$$ $$= P\{|X-Y| \leq 1\} + 2P\{X-Y \in (1,2]\}$$ where the last step follows because $X-Y$ has a symmetric distribution. NB: A random variable Z has symmetric distribution if  $$P(Z \leq z) = P(Z \geq -z) \quad \forall z \in \mathbb{R}$$  Thus the problem boils down to showing $$P\{X-Y \in (1,2]\} \leq P(|X-Y| \leq 1)$$ and I would be done. Unfortunately, I don't know how to proceed from here. I appreciate any help, hints, useful comments etc. I receive.

Doing a little reading over the break (The Probabilistic Method by Alon and Spencer); can't come up with the solution for this seemingly simple (and perhaps even a little surprising?) result:     (A-S 1.6.3) Prove that for every two independent identically distributed real random variables $X$ and $Y$,   $$Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1].$$


So I started a new campaign, where my players may go to other planes, which are described in the DMG. There are several planes, which has a nice side effect, which will change the PCs alignment. My question is: how to enforce a player to act like that alignment, which he/she become from that plane?

Lately, in one of my campaigns, I've been having problems with a character who everyone agrees is acting out of alignment. Everyone, that is, but him. The problem, of course, is that he's playing a Monk, and his actions are clearly chaotic in nature. Not just on rare occasions, either, but continuously. Well, I've told him that if he doesn't start acting more lawful, that his alignment will change. He, however, insists that I'm just trying to force him to play the character as I would play it.  How can I justify changing his alignment, without making it seem like I'm trying to control how he plays his character, or just pulling the GM card?  NOTE: I'm not asking for people to agree or disagree with mine or his view on the situation. Regardless of whether or not his actions justify a change of alignment does not matter, I simply want to know how GMs have in the past justified alignment changes, or how people would suggest going about doing so.


I'd like to get a Linux command which runs in the background and writes something to the terminal screen every one minute. I am trying to keep ssh session alive, I am using Cygwin for connection to the server but the connection is resetting every short time if nothing is written to the screen.  I already tried with sshd_config option to solve the short connection time by changing ServerAliveInterval 0 to ServerAliveInterval 60 but this does not solve the problem.

I found , but I'm sorry I don't quite understand the settings on the two variables ServerAliveInterval and ClientAliveInterval mentioned in the accepted response.  If my local server is timing out, should I set this value to zero?  Will it then never time out?  Should I instead set it to 300 seconds or something?  My question is simply, some of my connections time out when I suspend & then unsuspend my laptop with the response Write failed: Broken pipe and some don't.  How can I correctly configure a local sshd so that they don't fail with a broken pipe?


Easier to see via examples.  All of them with the following php version:  $ php --version PHP 7.4.4 (cli) (built: Mar 18 2020 04:33:54) ( NTS ) ...    Exhibit 1:  $ echo '<?php for ($i = 0; $i <= 10; ++$i ) {  print( (int)(100 * ($i + 0.7)) . "\n"); } ?>' | php 70 170 270 370 470 570 670 770 869  <<< uh? 969  <<< uh? 1070    Exhibit 2 replacing the type casting by float:  $ echo '<?php for ($i = 0; $i <= 10; ++$i ) {  print( (float)(100 * ($i + 0.7)) . "\n"); } ?>' | php 70 170 270 370 470 570 670 770 870 970 1070   The question is:   Why does the Exhibit 1 results happen?

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


I'm using a bib file to insert all my references. The bibliography is generated ok in the output. However, some references are shown between two pages (it means, the reference starts at the end of one page and it finishes at the beggining of the next). How can I do to make somekind of \newpage inside the bib file? I would like to show the entire reference information within the same page (not divided between two pages).  Raúl

My university's thesis guidelines require that each bibliographic entry appear in whole on a single page, rather than being split across two. How can I prevent (La)TeX breaking a paragraph across a page boundary?


As $p$ and $q$ are successive odd primes, for example if $p = 3$, $q = 5$ then  $p + q = 8 = 2 \times 4$ here 4 is a composite number. But how to prove it generally in all conditions?

Given the odd prime numbers,   Prove that if $x$ and $y$ are adjacent odd primes in this list, then $x + y$ has $3$ prime factors. The factors need not be distinct.  Here is an example I have provided: $3 + 5 = 8 = 2 \cdot 2 \cdot 2$. Therefore, $8$ has $3$ repeated factors of $2$.


Let $f_1(x_1), f_2(x_2)$ be polynomials in a single variable, of relatively prime degree, with complex coefficients. If $f_1(x_1)+f_2(x_2)$ is irreducible in $\mathbb C[x_1,x_2]$, then is it irreducible in  $\mathbb C[x_1,x_2,...x_r]$ for every $r\ge 3$ ?

It is a known fact that if $R$ is a UFD, then $R[X_1,X_2,\dots]$ is also a UFD, but there is a subtlety that is making me uncomfortable.  The standard approach essentially goes something along the lines of...let $f$ be a polynomial, so it only involves finitely many variables, say up to $X_1,\dots,X_n$. Then since $R[X_1,\dots,X_n]$ is a UFD, $f$ has a factorization into irreducibles. Then $f$ cannot have a factorization involving indeterminates $X_N$ not in $R[X_1,\dots,X_n]$. If it did, then $f$ would have two factorizations in the UFD $R[X_1,\dots,X_n,\dots, X_N]$, a contradiction.  This seems to assume that the prime factorization in $R[X_1,\dots,X_n]$ is still a prime factorization in $R[X_1,\dots,X_n,\dots,X_N]$. But how can you see that irreducibles in $R[X_1,\dots,X_n]$ are still irreducibles in $R[X_1,\dots,X_m]$ for $m>n$? This does not seem obvious.  Let $R_k=R[X_1,\dots,X_k]$. The explanantion I found is this: Suppose $p\in R[X_1,\dots,X_n]$ is irreducible in $R_n$. Suppose $p=ab$ for $a,b\in R_m$. Evaluating $X_1,\dots,X_n$ at $1$, you get  $$ \bar{p}=\overline{ab}\in R[X_{n+1},\dots,X_m] $$ But $\bar{p}\in R$, which implies that $a$ and $b$ do not involve any variables $X_{n+1},\dots,X_m$. So $a,b\in R_n$, and thus one is a unit, hence a unit in $R_m$.   The part I don't follow is how evaluation at $1$, implies $a$ and $b$ do not have indeterminates other than $X_1,\dots,X_n$. Isn't it possible that some of the higher indexed indeterminates disappear when you evaluate? Suppose for instance $p\in R_1$, and $a\in R_2$ is $a=-X_1X_2+X_2$. Then evaluting at $1$ gives $\bar{a}=0$ so we may not get the desired contradiction since $\overline{ab}=0\in R$?


Can I visit France with this Greek Schengen visa?

I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France?


Problem: find $\lim_{n \to \infty}\left(1+\frac{1}{n^2}\right)\left( 1+\frac{2}{n^2}\right)\cdots\left(1+\frac{n}{n^2}\right)$  My thought: Taking the log and we get $\sum_{k=1}^{n}\ln(1+\frac{k}{n^{2}})$. There is an inequality in another problem, which says: $$\frac{k}{n+k}\lt \ln\left(1+\frac{k}{n}\right)\lt\frac{k}{n}, \forall k \in N^{+} $$. So I think maybe I can use it here. Plug in $n^2$ and sum over k, we get $$\sum_{k=1}^{n}\frac{k}{n^2+k}\lt \sum_{k=1}^{n}\ln\left(1+\frac{k}{n^{2}}\right) \lt\sum_{k=1}^{n}\frac{k}{n^2}=\frac{1}{n^2}\frac{n(n+1)}{2}=\frac{n+1}{2n}$$ Anyway, the limit is $\sqrt{e}$(So if we take the limit of both sides of the above inequality, it should be$\frac{1}{2}$ and the right hand side is just right), but I cannot go further with the left side.   Any hint would be appreciated!

How can we compute the following limit:     $$\lim_{n\to\infty}(1+1/n^2)(1+2/n^2)\cdots(1+n/n^2)$$   Mathematica gives the answer $\sqrt{e}$. However, I do not know to do it.


I'm trying to rewrite a legacy php Browser-Based-Game so that it uses object oriented programming.  I find it relatively easy to model concrete nouns, like: new Npc(), new Character(), new Account(), new Clan().  I'm finding it more difficult to model a character's actions.  For example:    usable skills. a test for whether two characters are multiplayers attacking another character test for whether a character is allowed to attack another character etc.   Have you done something like this, and if so, what overall approach did you use to model the in-between-the-nouns behavior?

I'm new to game development and a bit confused about how to effectively store an object's access to certain spells/abilities.  The player and mob objects are all generated from the same class. However, each object may have access to different abilities and spells. How do I keep track of a specific object's access to these?  Example: My player object might have access to Fireball and Haste, while a goblin might have access to Confusion.  I followed , and I understand how to attach a spell function to scroll use. I'm just not sure how to emulate a character memorizing a spell and using it as an ability.


ls -l  total 36  -rwxrwxr-x 1 vips vips 8776 Jan 11 20:56 a.out     -rw-rw-r-- 1 vips vips   52 Jan 11 21:44 filemk.sh     drwxrwxr-x 2 vips vips 4096 Jan 11 22:14 hello     -rw-rw-r-- 1 vips vips 7174 Jan 11 09:23 installation.txt     -rw-rw-r-- 1 vips vips  928 Jan 11 22:26 linux_Commands     -rw-rw-r-- 1 vips vips  142 Jan 11 20:56 prog1.c   What does total indicate? Somewhere I read that it shows the number of blocks, but the number of blocks in my case is  1+1+2+1+1+1 = 7 .  Then what is it?

Apparently I cannot count. I think there are three files in /media  $ tree /media /media ├── foo ├── onex └── zanna 3 directories, 0 files   However, ls -l finds 12.  $ ls -l /media total 12 drwxr-xr-x  2 root root 4096 Jul 31 20:57 foo drwxrwxr-x  2 root root 4096 Jun 26 06:36 onex drwxr-x---+ 2 root root 4096 Aug  7 21:17 zanna   And, if I do ls -la I get only . and .. in addition to the above, but the count is total 20  What's the explanation?


I want to have a citation but I my citation I have word 'and' which is english however paper I am currently working on has to be in a different language thus my question is how to change this 'and' to equivalent word in different languages?     My code is:  \documentclass[10pt,a4paper]{article} \usepackage{polski} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx} \usepackage{fancyhdr}  \pagestyle{fancy} \fancyhf{} \usepackage[round]{natbib}    \bibliographystyle{plainnat}   \cfoot{\thepage} \renewcommand{\headrulewidth}{0pt} \renewcommand{\footrulewidth}{0pt} \renewcommand{\baselinestretch}{1.5}  \author{Nice} \title{Nice} \begin{document}     \section{Words on a printed page}         Some random words     \subsection{Words }    \newpage     %\nocite{*} %\bibliographystyle{amsplain} \bibliography{bibliografia.bib}  \end{document}   And sample bibliography entry:  @article{piketty2003income,     title={Income inequality in the United States, 1913--1998},     author={Piketty, Thomas and Saez, Emmanuel},     journal={The Quarterly journal of economics},     volume={118},     number={1},     pages={1--41},     year={2003},     publisher={MIT Press} }   Simple removal of the word "and" from bib files does not work.

I'm using natbib, german babel and natbib creates output of the form   Foo and Bar (1337)   I would like to get   Foo & Bar (1337) for citet and (Foo & Bar 1337) respectively for citep.


I have found a rather cheap Mamiya G 50mm f4 lens on ebay that has some tiny scratches on the rear element of the lens. Now, I have done some research on how much such scratches could affect the quality, but I have basically read everything from 'completely unusable' to 'absolutely no effect whatsoever'.   My question is: How much will such scratches generally affect the image? Will there be less of a problem since it is Medium Format? The scratches seem to be visible only from a certain angle as well.  The scratches are only really visible in the third image:

I have a lens with a small but significant looking scratch near the center. But I don't see any difference in the photos. Where does the imperfection show up? How important is it to get the piece of glass replaced? (It's a Panasonic 14-45mm micro 4/3 lens).


I know this is going to be crazy easy for someone, but I forget... what was the book series where the aliens attacked earth, wiped out a bunch of people, thought they were going to rule it so gave us a disease where girls were just as horny as guys so we could repopulate really quickly?

What I remember of this novel/series is that the main character creates solar laser satellites and mines asteroids to create more satellites to defend Earth from aliens. Later on, he uses the hollowed out asteroids as a base and eventually as an armored fortress to repulse the alien fleets. I last remember the main character attempting to hollow out more asteroids to defend and attack the aliens eventually.


I apologize for the simple question.  We have the text:     We will close this ticket, please reopen it or create new one if anything will be unclear or if you will have more questions.   But in my opinion it should be create a new one instead of create new one after taking a look at  post also.  Am I right? Which one is grammatically correct?  Thank you for your interest and time.

I wonder if there is a rule on that score. Judging from the examples below, it just looks as if you don't put a when one goes alone, and you have to use it when one goes with an adjective. Am I wrong?     We've run out of clean towels. - It's ok, I have a spare one.      I was looking for a clean towel but couldn't find one.      What towel would you like? - Just an ordinary one, I don't really   care.      Can I have a towel? - Go to the bathroom and take one.      Did you buy me a towel? - Yes, a big yellow one.


Do you have an example of a compact operator for which the image of the closed unit ball is not compact?

Let $X,Y$ be Banach spaces and $A\in\mathcal L(X,Y)$ . The task is to prove the following:  $A$ is compact if and only if the image of the closed unit ball in $X$ is compact in $Y$.  I have proven this when $X$ is a reflexive space.  Proof. Let $X$ be a reflexive space, $\bar B$ the closed unit ball in $X$, and $A$ a compact operator. Let further $y_n=Ax_n$ be a sequence in $A(\bar B)$.  In reflexive spaces $\bar B$ is weakly compact, so there exists a subsequence $x_{n_j} \to x$ weakly.  Because $A$ is compact, $Ax_{n_j}\to Ax$ strongly.   On the other side, $A(\bar B)$ is relatively compact, so there exists $z_k=Ax_{n_{j_k}}$ that converges strongly to $y\in Y$.  But $z_k\to Ax$ strongly. So by unicity of the limit $y=Ax$ and the image is compact.  It's easily proved that if the image is compact, the operator is also compact.  But I don't know what to do in case of nonreflexive spaces. Is there any counterexample or proof in such case?


It might be very useful to give users the possibility to mark/tag/signalize answers (and questions?) as "insecure", eventually even with a short notice why (SQL injection, outdated code that might create security risks, etc.). I think SO has a natural responsibility NOT to promote insecure code.  Especially highly upvoted php/mysql-questions/answers, some of them even wikis, are using critical/insecure/outdated code/tutorial links.  Note: This is not about outdated code, it's more about potential security risks.

I have a pretty active discussion on SO right now, about giving an answer, that could potentially harm the questioner. The question is  and discussion is in comments to .   In short, the OP asks for a way to implement a really dangerous thing. I've provided an answer to the question with a lot of warnings, while  told me that this is a very bad idea, and it is better to use prepared statements, and so on. He is absolutely right; I'm among those who upvoted his answer, but the question remains.   So, I would like to hear community's opinion on that topic. Should we protect others from shooting in their legs, or let them have responsibility to do it, if they want?  Update: One of my university teachers created  site (long ago). The idea of that site is to allow people training their SQL skills. I won't tell much about the site, you can register and check it out yourself (it is available in english), but the whole idea is just the same: execute SQL provided by the user. Of course it is fltered, checked that it is safe, placed in a sandbox, etc. But the concept is just the same. It's rather popular resource, it is on third place in  and have large and growing community. I hope this update will stimulate further discussion.


I was given the following problem in my assignment:     Define $a$~$b$ on the rationals by $a$~$b$ iff $b=ak^2$ for some rational number $k$.           Is ~ transitive?.       Please somebody explain to me how to do this problem. Thanks!

Just need some verification for this question or another way to approach it.  Given: a~b is defined on the rationals by a~b iff $b = ak^2$ for $some$ rational number $k$.  Is it reflexive? Symmetric? Transitive?(Show the Equivalence relation)  Reflexive: Must show that a~a   $a=ak^2$  $1=k^2$ which checks out. Its Reflexive  Symmetric: Must show that a~b and b~a  a~b: $b=ak^2$, $\frac ba$=$k^2$  b~a: $a=bk^2$, $\frac ab$=$k^2$  Not symmetric.  Transitive:   a~b and b~c than we must show that a~c  a~b: $b=ak^2$,  b~c: $c=bk^2$  a~c: $c=ak^2$  This is were I am sorta stuck not sure if I am allowed to do the following:  since $c=ak^2$ and $c=bk^2$ I can find that a=b?not sure any help would be appreciated.  Noticing that if zero is excluded then we would have an equivalence relation. However, when zero is included would symmetric fail and both reflexive and transitive still hold?


I have a script that sends a simple email at the end. When running it while my laptop is inside my university'e network, everything works just fine.  However, when I send an email from home using a command like this  mailx -s "test" me@icloud.com < mail-test   I can an error message as a return email saying      This is the mail system at host GZsMacbook2019.fritz.box.      I'm sorry to have to inform you that your message could not be   delivered to one or more recipients. It's attached below. ....   : host mx3.mail.icloud.com[17.172.34.65]   said: 550       5.7.1 Mail from IP 87.148.152.25 was rejected due to listing in Spamhaus       PBL. For details please see        (in reply to RCPT TO       command)   It looks like my IP is being blocked because it is listed in Spamhaus's data base. Spamhaus says this about the matter:     Deutsche Telekom advises against accepting e-mail from dialup IPs. We   provide these IP addresses dynamically to our customers for internet   access. Proper e-mail delivery should use dedicated servers, which is   why attempts of e-mail delivery from dialup-ranges generally can be   traced to compromised computers or other misuse.   (And, yes, my internet provider is Deutsche Telekom.)  But I need to send the email from a bash script that is executed hourly from cron. The email goes only to myself.  There is also a bit of explanations in Spamhaus' FAQ:   but that does not help.  I think, my home router (FritzBox) does actually run an MTA. And after trying out many of the solutions like the ones suggested at  or  , e.g., Ssmtp or sendmail, I really think the problem is that my IP address (which is assigned to me dynamically by my ISP) is being blocked.  I might be able to use the smarthost of my ISP, but then my script might not work anymore when my laptop is inside my university's network.  Is there any easy way I can send email from a shell script, no matter which network my laptop is in?  Thanks a lot in advance.

Using Raspbian and Ubunntu 16.04 LTS so need a generic Linux solution.  Requirement is simple:  I need a way to send one-line email messages from the command line.  I have set up a gmail account just for this particular Rpi3, with the address of rpi3abc@gmail.com - with no 2FA  So now I need to be able to send one-line mail messages from anywhere (including cron) without user intervention.    I also would like it to be able to send text files; basically, anything from stdin.


Hello I have to determine the gcd of $n^3+3n^2-5 $ and $ n+2$, but I can’t do it because I know we have to eliminate the $n$. I tried to eliminate $n^3 $ but I’m stuck for the rest.

$GCD(n^2+1,n+1)$,   $n\in \mathbb{N}$  What I did: $n^2+1=(n-1)(n+1) + 0$  So I thought  $(n^2+1:n+1)=n+1$  But that doesn't seem to be the case: $n=2$  $n^2+1=5$  $n+1=3$  $GCD(5,3)=1$  Why is the GCD here $n-1$?  E: I just realized (thanks to a comment) I made a mistake, as $n^2+1\neq(n+1)(n-1)$.  Edit2: I'm sorry guys, I don't understand most of your answers. We haven't yet studied things like the floor function in  my class. I know a bit of mod arithmetic and euclid's algorithm.


The last mod message I've seen is for December 6th, but there's been activity on the meta site since then with no notification in the diamond on the header bar. It's either specific to the Pets site, or to the beta sites, as I don't see this behavior on the Photography site where I also moderate.

Per  I'm posting this issue.  I'm a moderator over on Sci-fi & Fantasy.SE.  My moderator inbox missed :    The Meta Question in question should show up after the moderator message and before the new meta question, as it was posted on Jan 2 (it's currently Jan 6, so '2 days ago' is Jan 4).


I have the following problem:  Given a non-empty set $U$ and the power set $P(U)$. Proof $(P(U);\triangle, \cap)$ is a commutative ring. Which subset is the neutral and which one is the identity?   I have an idea of how to check if it's a ring (by checking all properties one by one) but I don't know how to deduce the neutral set and the identity.

I'm studying for an abstract algebra exam and one of the review questions was this:     Let $X$ be a set, and $\mathcal P(X)$ be the power set of $X$. Consider the operations $\Delta$ = symmetric difference (a.k.a. "XOR"), and $\bigcap$ = intersection.   a) Does $\Delta$ and $\bigcap$ make $P(X)$ into a ring?   b) If so, is it a ring with unity?   c) Is the ring commutative?   d) Is it a field?   For parts a) and b), I think it does form a ring with unity, but I'm not quite sure how to get started on proving it.   For part c), it is a commutative ring since $\mathcal P(X)$ is closed under symmetric difference and intersection, right?  Not even sure how to get started on d).  I'd really like to understand this question fully, so any kind of input would be tremendously helpful. Thank you!


I have data for a dependent variable, DV, representing a count of objects, with a range from 0 to 6 (sample size 450), slightly left skewed with a mode at 4:    Furthermore, I have a single categorical variable with three groups. I wish to perform a test to determine whether to reject the null hypothesis that the mean (or some other location measure) of the number of objects is the same across the three groups. ANOVA was suggested to me, but I believe this would be incorrect. However, could someone please confirm or correct my argument for this position?  The argument posed to me by the other party was that the DV is approximately normal and ANOVA is fairly robust to some deviation from normality. I disagreed with this position for the following reasons:   ANOVA requires a continuous DV at interval or ratio level. At first sight it may seem that count is ratio-level data, in that it has a true zero (you have zero items) and the intervals are equal. However, on , the definition of interval-level data and above includes:  "...their central characteristic is that they can be measured along a continuum..."  Going by a dictionary definition of "continuum", it would suggest a space in which you can observe values closer and closer to one another such that in the limit, the difference is almost imperceptible. Or another way of looking at it, two values are infinitely divisible. This is not the case for an integer variable such as a count of objects. As mentioned earlier, ANOVA requires (roughly) a normally distributed dependent variable with equal variance across the groups but is robust to some degree to nonnormality. However, I don't think an integer variable can validly be modelled with a normal distribution in that it can only hold integer values - even if it has a similar bell shape.   So anyway, because of point (1) I would have to conclude that count data is ordinal-level and a Kruskal-Wallis test would be better suited for this situation. However, it seems wasteful to treat counts as only ordinal, as the integer intervals are equal and there is a zero... so in addition to confirming or rejecting my arguments, any suggestions for other tests are welcome :-)

I am struggling with using the correct test for count data in R. The dataset I have is the number of nymphs produced by three aphid species on wheat.  So this is count data with one response variable (number of nymphs) and one explanatory variable with three levels (i.e. three different species).  I want to test whether there are any differences between the three species with the number of nymphs they produce.  I think that I should not use an ANOVA with count data. I have tried a GLM with QuasiPoisson, but I am struggling to interpret the output and be sure that I have used the correct test. Essentially I want to equivalent for a one-way anova but for count data.


I want to include the figure list and table list in the index of my article, similarly with others numbered sections. But, when I use the code below nothing happened. There are a way to do it?     \begin{document}      %-------------index-------------------- \newpage \tableofcontents \thispagestyle{empty}  \break  %---------figure list------ \listoffigures  \break  %---------table list------ \listoftables  \break               \end{document}

Is it possible to create a list of all the figures at the end of a document (this I can do) and make it appear in the table of contents?  So in the the table of content there will be a line saying List of figures ... 19 for example?


I have an Excel 2010 table that lists events, giving details about the event and a beginning and ending date for each event.  These events took place over the course of a year.  I need to create a list of all the dates within that time span (done already) and get a count for each day of how many events were happening on that date.  i.e. on June 4, 2017, there were 3 events.  So my original list would appear like this:    Event ID  Event Name  Start Date    End Date A12411    Event One   June 1, 2017  June 10, 2017 A45721    Event Two   June 1, 2017  June 5, 2017 A84541    Event Three June 2, 2017  June 4, 2017   etc...  And from the data above, I would like my list to show:  Date          Number of events June 1, 2017  2 June 2, 2017  3 June 3, 2017  3 June 4, 2017  3 June 5, 2017  2 etc...   I've tried Countifs, both regular and array versions, with no luck (it seems to count the occurrences on the first event, but not the other...) I tried an If(and()) construction, but had even less success (lots of #Values).  I COULD conceivably write a VBA function for it, but that seems like overkill, especially since this is the first time I've encountered this and don't see it being a recurring thing.

I have a formula which is like this  =COUNTIFS('sheet1 '!W:W,">0",'sheet1 '!A:A,"Truck")  which is count all data in column W (sheet1) larger than 0, which are called Truck in column A.  Now, I want this formula to read the same information but by consider a range of dates in between 1st of October to 15th (I have dates in Column B). Any input is greatly appreciate. Thanks


I am studying Unix and installed Ubuntu  but cannot update and I cannot solve, plz help me...  Problem  cannot update ubuntu18.10 by Err  What I did for solve  I know the artful does something wrong Searching some questions like this,  but I cannot find which line should be changed at all  deb http://archive.ubuntu.com/ubuntu artful main restricted$       6 # deb-src http://jp.archive.ubuntu.com/ubuntu/ artful main restricted$       7 $       8 ## Major bug fix updates produced after the final release of the$       9 ## distribution.$      10 deb http://archive.ubuntu.com/ubuntu artful-updates main restricted$      11 # deb-src http://jp.archive.ubuntu.com/ubuntu/ artful-updates main restricted$      12 $      13 ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu$      14 ## team. Also, please note that software in universe WILL NOT receive any$      15 ## review or updates from the Ubuntu security team.$      16 deb http://archive.ubuntu.com/ubuntu artful universe$      17 # deb-src http://jp.archive.ubuntu.com/ubuntu/ artful universe$      18 deb http://archive.ubuntu.com/ubuntu artful-updates universe$      19 # deb-src http://jp.archive.ubuntu.com/ubuntu/ artful-updates universe$   ()  could you explain me?  ERR MSG  E: The repository 'http://archive.ubuntu.com/ubuntu artful Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default.   E: The repository 'http://archive.ubuntu.com/ubuntu artful Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default.

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I am trying to use removeAttribute() to remove one specific class attribute from an element. The problem is that removeAttribute() seems to remove all of the other defined class attributes on the element.  Example:  HTML  Click

   CSS  .blue {   background-color: blue; }  .dotted {   border: thin dotted grey; }  .width-50 {   width: 50px;   height: 50px; }   JS  var el = document.getElementById('click'); el.addEventListener("click", removeColor, false);   function removeColor() {     var box = document.getElementById('box');     box.removeAttribute('class', 'blue'); }   How can I just remove the one class attribute from the element, without affecting the other class attributes on the element?

How can I change the class of an HTML element in response to an onclick or any other events using JavaScript?


I'd like to add markers to my plots only at certain y levels. How to do this for certain x levels is obvious, I didn't manage to do it inversley though.  What I have (equi-x):    What I want is something like this (equi-y):    My code:  \documentclass[10pt,a4paper,oneside]{scrreprt} \usepackage{tikz}                    \usepackage{pgfplots}            \pgfplotsset{compat=1.8}  \begin{document} \begin{tikzpicture}  \begin{semilogyaxis}[     cycle list name=exotic,     xlabel=$E_S/N_0\;(dB)$,     ylabel=$BER\;(\%)$,     ytick={0.0001,0.01,1,100},     xmin=0,     xmax=40,     ymin=1e-4,     ymax=100,     legend pos=outer north east,     legend cell align=left,     grid=major,                                                  height=6cm,     width=0.8\textwidth ]             %% READ DATA \pgfplotstableread[     header=false,     comment chars=! ] {ber.dat}\berdata  %% PLOT DATA % Workaround for line colors, doesn't work with \foreach \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=1]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=2]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=4]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=5]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=7]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=6]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=8]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=9]  {\berdata}; \addplot +[smooth, mark repeat={10}, line width = 1.0pt] table[x index=0,   y index=10] {\berdata};  %% LEGEND \legend{BPSK,QPSK,16-QAM,16-QAM,32-QAM,64-QAM,256-QAM,1024-QAM,4096-QAM} \end{semilogyaxis} \end{tikzpicture} \end{document}   ber.dat can be downloaded here, if you like:   Edit1:  Managed to find a workaround:    By calculating the inverse function values with MATLAB and plotting them on top.  %% READ DATA \pgfplotstableread[     header=false,     comment chars=! ] {plotdata/ber_markers.dat}\bermarkers         \pgfplotsset{cycle list shift=-9}  \addplot +[smooth, only marks, line width = 1.0pt] table[x index=1, y index=0]  {\bermarkers};                   %\addplot +[smooth, only marks, line width = 1.0pt] table[x index=0,    y index=3]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=2, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=4, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=5, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=7, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=6, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=8, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=9, y index=0]  {\bermarkers}; \addplot +[smooth, only marks, line width = 1.0pt] table[x index=10,y index=0]  {\bermarkers};     Christian: Thanks for your work by the way, it is extremely useful.

I'm trying to put some arrows on the left and right side of the maximum of a curve. The arrows should point along the curve. My problem is that if I use the [pos=X] notation I don't know where I am in relation to the maximum. And if I use absolute coordinates the node is not sloped.   \documentclass{article} \usepackage{pgfplots} \usetikzlibrary{shapes.geometric} \pgfplotsset{compat=1.7}  \begin{document} \begin{tikzpicture} \tikzset{myarrow/.style=          {sloped,isosceles triangle,anchor=apex,fill=black,inner sep=2pt}} \begin{axis} \addplot [smooth] {-x^2}  node[pos=0.4,myarrow,rotate=180]{} %ok  node[pos=0.6,myarrow]{}; %ok  \addplot[smooth,green] {-x^2+2*x-4}  node[pos=0.4,myarrow,rotate=180]{}  node[pos=0.6,myarrow]{} %wrong side  node[myarrow,fill=red] at (axis cs:4,-12){}; %wrong rotation! \end{axis}  \end{tikzpicture}  \end{document}     Edit: Some remark about Jake's answer  Jake's code (naturally) works but    for my case it is a bit too complicated. Jake gets the correct rotation for the arrow by drawing a short path from x-1pt to x (cool idea). He gets the coordinates for this small path with intersections. But as my plot is based on a function I can simply calculate the values (e.g. with \pgfmathparse) and then draw the small path after the plot:  \path  (axis cs:3.99,-11.94012) -- (axis cs:4,-12) node[pos=1,myarrow]{};   The same can also be achieved by redrawing the plot but with a restricted domain:  \addplot[draw=none,domain=3.99:4] {\MyFunction{x}}  node[pos=1,myarrow,fill=yellow]{};  I also looked if there is a way to decide where I am relative to the maximum (so that I can change the rotation) and in theory it is possible: If I use the code found here  \pgfplots@metamax is known after the plot and can be used in calculations.


I feel like I have found an amazingly rude user on the SE network. I would like to file a complaint about that user but I don't know what that user needs to have done wrong or how to do it.  This user has not done anything wrong on the surface, but often blatantly disrespects comments against himself. How and should I attempt to get rid of that user?

I think the community does a great job policing questions/answers, etc. and the community has some good tools available to do this.  Between flagging questions with some reasons behind it and editing posts, closing them, and deleting them, the only thing that seems to be missing to me is the ability to flag a user.  Reasons to flag a user as abusive:   Duplicate User Abusive Behavior Offensive user name or profile User profile consists of spam Others?


I have a div which I'm using as a submit button for my form, but I cannot figure out how to center it. When the margins are set to auto, it ends up being just slightly right off the center of the page and of other divs with the same css style.    #submit {  background-color: blue;  height: 80px;  width: 720px;  margin: 0 auto;  text-align: center; } <form name="algForm">

 </form>     Thanks.

How can I horizontally center a
 within another
 using CSS?

Foo foo


In my textbook, we have the following truth table:   $P$ true and $Q$ true means that "$P \implies Q$" is true. $P$ true and $Q$ false means that "$P \implies Q$" is false. $P$ false and $Q$ true means that "$P \implies Q$" is true. $P$ false and $Q$ false means that "$P \implies Q$" is true.   I'm confused by what this means? I don't see why $P$ true and $Q$ false is the only combination that gets us that false and the rest of them get us true. Could anyone help clarify what's going on? Why is what is in the textbook correct? Thanks.

Is there a proof for the logical equivalence of $a \rightarrow b$ and $\lnot a \vee b$?


I know that ghost fields de-couple from the gauge fields in abelian QED. But my question is how does decoupling prove that we cannot observe ghost fields?

I was studying the path integral quantization of non-abelian gauge field. After the path integral quantization, the action becomes  $$\mathcal{L}=-\frac{1}{4}F^a_{\mu\nu}F^{a\mu\nu}-\frac{1}{2\zeta}(\partial_{\mu}A^{\mu a})^2 +\partial^\mu\bar c^a(D_{\mu}c)^a$$  Feynman rules for antighost-ghost-gauge boson vertex (e.g. $SU(2)$ gauge boson) is $-g \epsilon_{abc}p_\mu$. I can't understand why there is no process with ghost in external line.(For example, two gauge bosons annihilate and become ghost and antighost. I can certainly calculate the amplitude for this diagram according to Feynman rules. )   Certainly I know ghost is unphysical so should not exist in external line. But I want to know whether no external ghost line can result from the theory itself (like the amplitude of this process can be canceled by some other process?) or is just an axiom that we put on this theory?