Centos Your PHP MySQL library version 1.5.73 differs from your MySQL server version 5.5.39
Centos mysql version is 5.5 however PHPmyadmin still says version 5.1
Can I concatenate multiple MySQL rows into one field? Using MySQL, I can do something like:  SELECT hobbies FROM peoples_hobbies WHERE person_id = 5;   My Output:  shopping fishing coding   but instead I just want 1 row, 1 col:  Expected Output:  shopping, fishing, coding   The reason is that I'm selecting multiple values from multiple tables, and after all the joins I've got a lot more rows than I'd like.  I've looked for a function on  and it doesn't look like the CONCAT or CONCAT_WS functions accept result sets.  So does anyone here know how to do this? intuition on the fundamental group of $S^1$ I am familiar with the proof that the fundamental group of the unit circle $S^1$ is $\mathbb Z$, yet I couldn't develop intuition for why it is true. For example, why would I fail if I try to find homotopy from a path that circles $S^1$ once to the path that stays at one point all the time? What brakes the continuity of such a homotopy? How can I display only the unique values in one column in Excel? Is there a way to display the unique values in a column ONLY?  Example:   AAPL AAPL AAPL AAPL AKAM AMZN AMZN AMZN AMZN AMZN AMZN  Expected result:   AAPL AKAM AMZN  I have already done a sort for multiple factors, and the first match for each is the best match.  I'm not sure if this is a vlookup or something else. .NET - How can you split a "caps" delimited string into an array? How do I go from this string: "ThisIsMyCapsDelimitedString"  ...to this string: "This Is My Caps Delimited String"  Fewest lines of code in VB.net is preferred but C# is also welcome.  Cheers! If $a^{n}-1$ is prime then $a=2$ and $n$ is prime? I was doing some basic Number Theory problems and came across this problem :     Show that if $a$ and $n$ are positive integers with $n\gt 1$ and $a^{n} - 1$ is prime, then $a = 2$ and $n$ is prime   My Solution : (Sloppy)        $a^{n}-1$ = $(a-1)$ . $(a^{n-1} + a^{n-2} + ... + a + 1)$   This means that $(a-1)$ | $(a^{n}-1)$    But $(a^{n}-1)$ is prime   So , $(a-1)$ = 1 $\Rightarrow$ $a = 2$   Now , let $n$ be composite   $n = kl$ , where $1 \lt k \lt n$ and $1 \lt l \lt n$   Now , $a^{kl}-1$ = $(a^{k}-1)$ . $(a^{k.{(l-1)}} + a^{k.{(l-2)}} + ... + a^k + 1)$   This means that $2^{n} -1$ is composite    Hence , we have achieved a contradiction      My Question : Am I correct ? I'm studying abstract algebra for the first time.  let $F$ be a field. I learned that polynomials over field $F$ means polynomials with coefficients in $F$ (denoted by $F[x]$). But when I keep studying, I get to confused the word, 'polynomial functions from $F$ to $F$'.  Firstly, I consider this as induced functions from $F[x]$, so I guess all coefficients of these functions are in $F$. But let $F_{4}$ be a finite field consisting of four elements $\{0, 1, a, b\}$. and let $f: \{0,1\} \rightarrow \{0,1\}$ be a function defined by $$ f(x)=ax^2-ax$$ Since $\{0,1\}$ is a subfield of $F_{4}$ and $f(0)=0, f(1)=0$, I think $f$ is a example polynomial functions from $F$ to $F$ of which coefficients are not in $F$. Am I wrong? if so, please help me.  I encounter this problem while solving 'the set of all polynomial functions from $\Bbb{Z_{3}}$ to $\Bbb{Z_{3}}$ cannot possibly be isomorphic to $\Bbb{Z_{3}}[x]$'. Why are properties lost in the Cayley–Dickson construction? JavaScript open in a new window, not tab I have a select box that calls window.open(url) when an item is selected.  Firefox will open the page in a new tab by default.  However, I would like the page to open in a new window, not a new tab.    How can I accomplish this? In the IEEE 802.3 frame structure there is a 7 byte preamble section for synchronization. If it is really for synchronization does that mean Ethernet is synchronous and not asynchronous?    Ethernet structure for reference: How handicapped am I in graduate admissions if I graduated from a lower tier university? Due to a combination of factors, I ended up going for my undergraduate studies to a relatively unknown university that was close to me geographically.  Let's say that I have a relatively standard background for someone trying to apply to top tier schools for graduate studies (some research experience, some low to medium quality publications, very strong grades, good recommendation letters). Then how much does the alma mater have an impact for someone like me? I obviously know that it is still possible to be accepted, but how much of a disadvantage am I looking at exactly? passive Vs active or omission of 'which is' What is the part of speech of 'regarded' in the following?     "a quality of beauty and intensity of emotion regarded as characteristic of poems"    Why isn't it "... [which is] regarded ..."?  And in another case:      "a small lizard with wide feet, found especially in warm countries"     And also:      "Words used to describe writing or speech style"    In all these examples, why shouldn't the verbs be in their passive form (e.g. which is found, words that are used)?   I am a ESL learner and I am very confused by these usages! Relay: higher voltage allowed at lower current? Is it safe to use a 30VDC/1A relay for a voltage of 60V but a current of &lt;100uA? E.g. this one: What's the added value of SD line over regression line when examining association between 2 variables? I'm trying to incorporate different practices to use when exploring a new data set. Especially, how to examine the association between two variables.  Steps for example (not necessarily by order):   plot a y-by-x scatter plot of the raw data to see the relationship visually. compute summary statistics for each variable (mean and sd) compute correlation coefficient r draw the OLS regression line, compute its slope and intercept etc....   I've come across the "SD line" in Freedman's Statistics book, which is defined as:     "the line that goes through the point of averages and climbs at the rate of one vertical SD for each horizontal SD" Freedman, D., Pisani, R., &amp; Purves, R. (2007). Statistics (4th edn).   Since this book ("Statistics") is a canonical textbook, I consider its choice to discuss the SD line as an indication for the line's importance. However, a simple google search for the term "SD line" doesn't yield as many independent results. Most of them come directly from Freedman's book. This tells me it's not a central concept in bivariate analyses in general.  When comparing the SD with the OLS regression line, it seems like the regression line is more informative (than the SD line) for predicting y from x. Therefore, I'm wondering if bothering to plot the SD line has any benefit or added value that I would not already have when plotting the regression line.  Example using mtcars dataset, focusing on association between weight and mpg  data(mtcars)  ## calculate means mean_wt &lt;- mean(mtcars$wt) mean_mpg &lt;- mean(mtcars$mpg)  ## calculate standard deviations sd_wt &lt;- sd(mtcars$wt) sd_mpg &lt;- sd(mtcars$mpg)  ## scatter plot plot(x = mtcars$wt, y = mtcars$mpg)  ## add the "point of averages" points(mean_wt, mean_mpg, col = "red", cex = 1.5, pch = 16)  ## calculate the slope of the sd line slope &lt;- -1*sd_mpg/sd_wt  ## plot the sd line curve(expr = x*slope + (mean_mpg - slope*mean_wt), add = TRUE, col = 'blue', lwd = 2, type = "l", lty = 2)  ## plot the regression line model &lt;- lm(mpg ~ wt, data = mtcars) abline(model, col = "orange", lwd = 2)  ## legend legend("topright",        legend = c("Regression line", "SD line"),        col = c("orange", "blue"),        lty = c(1, 2),        lwd = c(2, 2))     Thus, my question: how can the SD line increase one's understanding about the relationship between two variables, in a way that's either adding or complementing on what the regression line already tells? How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions If $n$ is an integer and $n&gt;2$, then $$\bar{z}=z^{n-1}$$ has $n+1$ solutions. Does this have something to do with the rational root theorem? Differential form is closed if the integral over a curve is rational number. The following problem comes from do Carmo's book Differential Forms and Applications, Chapter 2, Exercise 4:  Let $\omega$ be a differentiable 1-from defined on an open subset $U\subset \mathbb{R}^n$. Assume that for each closed differential curve $C$ in $C$, $\int_C \omega$ is a rational number. Prove that $\omega$ is closed.   Can anyone give some hints? My idea was that we could try to show the integral vanishes if the curve lies in $N_\epsilon (p)$ (i.e. a small neighborhood around $p$) for any $p$ in $U$ and use the Poincare Lemma, but failed. Given two ciphertexts $c_1 = enc(p_1)$ and $c_2= enc(p_2)$ using any additive homomorphic encryption scheme (or specifically Paillier).   Can we find out whether the underlying plaintexts $p_1,p_2$ are equal without decrypting $c_1,c_2$ i.e. homomorphically? Override back button to act like home button What can I do if I forgot my Windows password? Equation with high exponents I was surprised to find that standalone package can not compile a document with an equation:  \documentclass{standalone} \begin{document} \begin{equation} % not working! F(V, T) = E(V) + D(T) \end{equation} \end{document}   Is there an option or some workaround that allows this? The current error is something like:   ! Missing $ inserted.   in line 4. (The idea of course is that the including (main) document can just \input the standalone without knowing if is going to be an equation or something else)