Another question about how to learn algebraic geometry...
Best Algebraic Geometry text book? (other than Hartshorne)
How to get remote host DNS address from a super-slim host (docker) without ping or bind-utils? I no longer need an answer to a question; what should I do to the question? Are {/bin, /lib, /sbin} symlinks into /usr in Ubuntu? I do not have access to an Ubuntu system or chroot. I was hoping if someone could tell me if the  is accurate in saying:     For Quantal, merged /usr should be supported. On new systems installer should create {/bin, /lib, /sbin} symlinks into /usr. I am trying to show that if $n$ is an odd natural number, then $8$ divides $n^{2}-1.$ I was able to prove that because I know that if $n$ is an odd natural number, then $n^{2}$ can be written as $8k+1$ for some $k\in \mathbb{N}.$ I would like to show this question by using the Euclidian division. Then I wrote $n^{2}-1=8k+r$, where $0\leq r  &lt; 8.$ When $r=2$ we get $n^{2}-1=8k+2.$ Since $n$ is odd, then $n^{2}-1$ is even and I got stuck. Is there way to fix that? Correcting for multiple kruskal wallis tests I am running a kruskal wallis test a number of times (37) and wanted to know if I have to adjust the p-values of the kruskal tests before I look any further into the post hocs? I can't seem to work out the inequality $(\sum |x_n|^q)^{1/q} \leq (\sum |x_n|^p)^{1/p}$ for $p \leq q$ (which I'm assuming is the way to go about it). How do I install an older version of an app on an iPhone? I have append a mesh (rex) from this .blend .  In edit Mode I see different vertices from objcet mode (see pictures). The vertices of belt are missing!  OBJECT MODE:   EDIT MODE:   How can I edit vertices of belt? Is It a bug?  This is my .blend  maybe can help. Code breaks when updating jQuery due to changes in toggle What is the meaning of “runneth” in ? Possible Duplicates:             does anyone know a free software that will graph the directories on my hard drive and sort them in order of largest size?  or provide me a solution for me to quickly determine what drives/ files are consuming my hard drive space? In a sentence taken from the Oxford Dictionary:     ‘The inscription on his tombstone in Groombridge Church, where he is buried alongside his three children, bears his original name and no reference to his nom de plume.’   Is ‘buried’ an adjective, a , or a   because it follows the copular verb is?      Predicate nominatives complete only linking verbs. The linking verbs include the following: the helping verbs is: am, are, was, were, be, being, and been; the sense verbs: look, taste, smell, feel, and sound; and verbs like become, seem, appear, grow, continue, stay, and turn.   Or is it a past participle because the clause is in the passive voice?   Does “he is buried” mean currently his body lies in a coffin covered with soil, or  does it mean he has been buried by someone?  If we say ‘he was buried’ it clearly refers to an event that happened and ended sometime in the past. It might even suggest that the burial ground has since been changed. Confidence interval around binomial estimate of 0 or 1 What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$? In the following sentence:     The city is populated by many people.   "many" can be replaced by something like "a great number of" (let us leave the perceived differences between the meanings of these two modifiers out of discussion):     The city is populated by a great number of people.   I understand that this replacement does not change the object "populating the city" from the original "people" to a "number", but rather shows the ability of expressions in the form "[numeral] of" to provide information about the quantity of nouns they modify.  Is this ability due to some special qualities of nouns such as "number", "quantity", "fraction", &amp;c., or is it just one usage of the preposition "of"? Why lipophilic molecules can pass phospholipid bilayer, in spite of 2 hydrophilic layers? It is commonly told that, hydrophobic/ lipophilic/ nonpolar molecules can quite easily pass phospholipid bilayer, and hydrophilic (polar or ionic) molecules can't pass (when no protein aid that); because hydrophobic nature of the lipid.  But in the same logic, hydrophobic molecules shouldn't pass through the bilayer. Because there are 2 hydrophilic layers in the membrane. i.e.      A and A' .  Then how the hydrophobic molecules can pass through A and A'?   I guess, it is due to thin diameter of A and A' . Is that? This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this?   More formally, suppose I ran the following two regressions:  $$ y_1 = X_1\beta_1 + \epsilon_1 $$ and  $$ y_2 = X_2\beta_2 + \epsilon_2 $$ where $X_i$ refers to the design matrix of regression $i$, and $\beta_i$ to the vector of coefficients in regression $i$. Note that $X_1$ and $X_2$ are potentially very different, with different dimensions etc. I am interested in for instance whether or not $\hat\beta_{11} \neq \hat\beta_{21}$.   If these came from the same regression, this would be trivial. But since they come from different ones, I am not quite sure how to do it. Does anyone have an idea or can give me some pointers?   My problem in detail: My first intuition was to look at the confidence intervals, and if they overlap, then I would say they are essentially the same. This procedure does not come with the correct size of the test, though (i.e. each individual confidence interval has $\alpha=0.05$, say, but looking at them jointly will not have the same probability). My "second" intuition was to conduct a normal t-test. That is, take   $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11})} $$  where $\beta_{21}$ is taken as the value of my null hypothesis. This does not take into account the estimation uncertainty of $\beta_{21}$, though, and the answer may depend on the order of the regressions (which one I call 1 and 2).   My third idea was to do it as in a standard test for equality of two coefficients from the same regression, that is take  $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11}-\beta_{21})} $$   The complication arises due to the fact that both come from different regressions. Note that   $$ Var(\beta_{11}-\beta_{21}) = Var(\beta_{11}) + Var(\beta_{21}) -2 Cov(\beta_{11},\beta_{21}) $$ but since they are from different regressions, how would I get $Cov(\beta_{11},\beta_{21})$?  This led me to ask this question here. This must be a standard procedure / standard test, but I cound not find anything that was sufficiently similar to this problem. So, if anyone can point me to the correct procedure, I would be very grateful! A mysterious app named &quot;10102&quot; shows up in my data usage. It bears only the standard Android app icon (the Bugdroid logo with a cube on its torso). From what the graph tells me, it has used 36 megabytes of data in the background and zero on the foreground. I think I haven't uninstalled anything for months. Is it malware? I haven't sideloaded anything and only authorized my laptop as a USB debugger. If it's malware, how do I remove it? I have no idea how to find its package name and 10102 isn't in the list of downloaded apps in settings. I'm running stock &amp; never-been-rooted Android 4.4.4 on Nexus 4. How to remove chromium-browser settings from Ubuntu 14.04? I have already gone through   and I'm really not getting why the solutions given there are not working for me.  What I'm doing is:   sudo apt-get purge chromium-browser   rm -rf ~/.config/chromium     Then reinstalling by running the following command:   sudo apt-get install chromium-browser    This must remove the settings of chromium-browser and do a fresh installation. The browser is uninstalling, but after being installed it is containing the previous settings, moreover it's not signing me out of even Gmail! Should I use OLS of fixed effects for this model for estimating level of immigrants? I'm trying to estimate this model on immigration levels I found in a paper and I'm not sure if they used OLS or fixed effects, it says that its a simple OLS but then mentions adding the country fixed effects. can someone help? completing the square for Gaussian multivariate estimation I have been trying to derive the posterior distribution in the case of weighted Bayesian regression in the case of multivariate normal distribution for a few days and have been stuck. I am not sure if this is due to lack of my linear algebra skills or if I have done something really wrong.  In my case, the distributional assumptions are:  $$ y = N (B x, W^{-1} \nabla) $$  The parameters $B$ have a normal prior.   $$ P(B) = N (B_0, \Sigma_{B}) $$  The conditional posterior distribution for $B$ is proportional to $P(y|B) P(B)$. This is proportional to:  $$ \exp \big((B - B_0)^T \Sigma (B - B_0) + (y - Bx)^T \nabla (y - Bx)\big) $$  I have seen the textbooks mention something called completing the square which as far as I can tell equates to matching like terms. Even though I could work out for scalar variance terms, I am having trouble figuring out how to deal with the precision matrices and how this can be decoupled.   [EDIT]:  So, I tried to make a run with Glen_b's suggestion and came this far:  Original expression without the exponential (I will simplify notation slightly):  $$ (B - B_0)^T \Sigma (B - B_0) + ( y - Bx)^T \nabla (y - Bx) $$ Expanding:  $$ B^T\Sigma B - 2 B_0^T \Sigma B + B_0^T \Sigma B_0 + y^T \nabla y - 2 y^T \nabla B x + (Bx)^T \nabla Bx $$  $$ = B^T(\Sigma + x^T \nabla x)B - 2 (B_0^T \Sigma B + y^T \nabla B x) + C $$  So I am not sure how to make further progress with the second term. I guess I have to make it in the form 2(some_term)B but not sure how that can be done.