I am confused about whether I should write "I work at registrar's office" or "I work in registrar's office"
When do you use at the office? And when do you use in the office? What's the difference between the phrases?
In Java, is there any way to use the JDK libraries to discover the private classes implemented within another class? Or do I need so use something like asm? Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon&gt;0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck. How to mount read-write an ext4 partition on Windows? I want to use ext4 on my external HDD, but it must be cross-platform. (At least Linux, Win7 &amp; WinXP).  Unfortunately, I haven't found any proper driver allowing Windows to WRITE to ext4. I've found , but it only reads ext4.     9. ext4 extent read-only, no  size truncating and expanding support   More:     Supported Ext3/4 features:         flexible inode size: > 128 bytes, up to block size   dir_index:    htree directory index   filetype:     extra file mode in dentry   large_file:   > 4G files supported   sparse_super: super block backup in group descriptor   uninit_bg:    fast fsck and group checksum   extent:       reading, writing with no extending.   journal:      only support replay for internal journal         Unsupported Ext3/4 features:         journal: log-based operations, external journal   extent: size truncating &amp; expanding, file deletion   flex_bg: first metadata group   EA (extended attributes), ACL support      Also, I have found a patch for Ext4Fsd v0.50 ():     New: Matt Wu has made a new release 0.50 at   ext2fsd.com.  Support for ext4 extents and fix   for BSOD on Windows 7.   I don't think it will be safe. Also I've read some words about writing ext4 in Windows could cause data loss on the disk...  What is the External HDD used for? - First, it will store backups, then family movies, pictures. Some music, and etc. It will be connected to a Raspberry Pi, if I finally receive it. It won't really move, just when it is used to migrate computer's data to a new one. The largest files it will store are Clonezilla disk images (I don't know, if they will be large files or not).  Can someone provide a solution for this problem? Or is there NO important enough difference between ext4 and ext3, and I should use ext3? - (If yes, then can I use Ext2Fsd for that ext3 mount?)  Thank you! Mod of numbers with large exponents [modular order reduction] I find that at the end of a long day, I sometimes have a large number of programs running. All which I will need to use tomorrow. Normally, this isn't an issue, I can simply lock the machine and come back tomorrow. My problem arrises when windows update launches in the middle of the night and force restarts my computer. That in turns closes all my open software. I of course save everything regularly so I don't loose anything, but I waste time reopening all of those resources whenever there is a restart.   [EDIT]  I should clarify that I still want to be able to restart my computer when an update comes down. Preventing the restart only delays the problem until later. I should have been more specific in that I want to be able to recover my working environment after a restart for any reason. Things like scheduled maintence, power loss, updates, and software installs.  [EDIT]  I can't simply have them setup to launch at startup becasuse those files change from week to week. So I need something that monitors what I have open, and gives me the option to "recover" those software sessions when I log back in.  Anyone have any suggestions on what I can do? I'd even be willing to purchase software to do this for me if that is the only option.  Thanks Is Object constructor called when creating an array in Java? In Java, an array IS AN Object. My question is... is an Object constructor called when new arrays is being created? We would like to use this fact to instrument Object constructor with some extra bytecode which checks length of array being constructed. Would that work? MySQL Replication : 1 Slave / Multiple Masters I have the following element element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)  I want to assure the text on this filed is TESTUSER, so I tried:  expect(element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getAttribute('value')).toEqual('TESTUSER');  then I got the error: Expected null to equal 'TESTUSER' So I tried: element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getText().then(function (value) {         console.log(value);       })  And I got this error: Expected '' to be 'TESTUSER'.  How to get the value of this field and expect it is TESTUSER? My mom and I are having a dispute on much more easy versus much easier. For example, consider the sentence:     It's [much more easy]/[much easier] to do action X than action Y.   I say that much easier is correct and that much more easy is grammatically incorrect, while she says that both are okay. I understand that both are acceptable colloquially, but which is grammatically correct here? If you could explain why, that would be even better! Best Algebraic Geometry text book? (other than Hartshorne) What is Peter Quill's status after Guardians of the Galaxy Vol. 2? Suppose I am given a morphism of schemes $f: X \longrightarrow Y$ and suppose that for any point $y \in Y$, $\kappa(y)$ denotes the residue field. I would like to show that the fibered product $$X \times_{Y} \text{Spec}(\kappa(y))$$ is homeomorphic to the preimage $f^{-1}(y)$ in the induced topology.  The following is my attempt so far:  The question is obviously affine on the target, so without loss of generality we reduce to the case of a morphism $f: X \longrightarrow \text{Spec }A$. Then we have  $$ f^{-1}(\text{Spec }A) = \bigcup_{i \in I} \text{Spec }B_{i} $$ via morphisms $$ \phi_{i}: A \longrightarrow B_{i}. $$ We can then write, \begin{align*} f^{-1}(\text{Spec } A) \times_{\text{Spec } A}\text{Spec } \kappa(y) &amp;= \bigcup_{i \in I} \left( \text{Spec } B_{i} \times_{\text{Spec }A} \text{Spec }\kappa(y) \right) \\  &amp;= \bigcup_{i \in I} \text{Spec }  \left( B_{i} \otimes_{A} \kappa(y)  \right). \end{align*} Now let $\mathfrak{p}$ be the prime ideal of $A$ corresponding to the point $y \in \text{Spec } A$. Then $\kappa(y) = (A/ \mathfrak{p})_{\mathfrak{p}}$. Then for any of the $B$ (dropping the index for brevity), we have \begin{align*} B\otimes_{A} (A/ \mathfrak{p})_{\mathfrak{p}} &amp;\simeq B \otimes_{A} A / \mathfrak{p} \otimes_{A} A_{\mathfrak{p}} \\ &amp;\simeq B_{\mathfrak{p}} \otimes_{A} A / \mathfrak{p} \\ &amp; \simeq B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}} \end{align*}  Now the prime ideals in $B_{\mathfrak{p}} / \mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$. Further, the prime ideals of $B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B$ contained in $\phi(\mathfrak{p})B$. That is, we have \begin{align} \text{Spec }B_{\mathfrak{p}} &amp;= \{  \mathfrak{q} \subseteq B :  \phi^{-1}(\mathfrak{q})  \subseteq \mathfrak{p}  \} \\ &amp;=  \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \}. \end{align} Note that in the very last line we have abused notation slightly: There is not really any notion of being "inside" $\mathfrak{p}$ when it is being treated as a point in the scheme. So really we mean that $f(\mathfrak{q})$ is a point in the scheme whose corresponding prime ideal is a subset of $\mathfrak{p}$. Now as we said above, the prime ideals of $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ are the following $$ \text{Spec }(B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}) = \{ \mathfrak{q} \subseteq B : f(\mathfrak{\mathfrak{q}}) \subseteq \mathfrak{p}      \text{ and } ???  \} $$ This is the point at which I get stuck. Ideally I would like to make some argument from the statement "Now the prime ideals in $B_{\mathfrak{p}}/\mathfrak{p}B_{\mathfrak{p}}$ correspond precisely to the prime ideals of $B_{\mathfrak{p}}$ containing $\mathfrak{p}B_{\mathfrak{p}}$" to conclude that the question marks are the condition $\mathfrak{p} \subseteq f(\mathfrak{q})$. Could someone point me in the right direction as to how to get this condition?   Is the proof up until this point correct? Different sources online seem to do this many different ways, so it's difficult for me to check. Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as:  $$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$  How can I prove the Fisher Information Matrix is positive semidefinite? Make IN clause behave like AND clause I've asked the same question on , but got no answer, so that's why I'm asking it here (I've read that simple sql questions should be asked at SO, but I have no choice).  Suppose I have 3 tables: posts, post_categories and categories. I'm implementing some kind of page with filters where I can filter posts by categories. User can select multiple categories. When he selects more than one, they should be summed. I can't get it working. What I have now is simple IN() SQL clause:  SELECT posts.id, post_categories.category_id FROM posts  JOIN post_categories ON posts.id = post_categories.post_id  WHERE post_categories.category_id IN (1,2,3) LIMIT 10;   But it is not matching all ids, it is OR and I need AND. What I need here is to find all posts that have categories with id=1 AND id=2 AND id=3, but instead this query returns posts that have at least one category from the IN() list. Reason of existense of the extra space in align environment and removal of it between two align environments This is a follow-up question regarding the extra vertical space in amsmath's align environment. Why when in use align uses so much vertical space in contrast with other environments like for example tabular or itemize?  \documentclass[12pt]{article} \usepackage[top=0.3in, bottom=1.2in, left=0.8in, right=0.8in]{geometry}   \usepackage[fleqn]{amsmath} \usepackage{unicode-math}  \setlength{\mathindent}{0cm} \newcommand{\3}{\vspace{0.3cm}}  \title{} \author{} \date{}  \begin{document}  70  \begin{align*} &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}  80  \begin{itemize} \item Item 1  \item Item 2  \end{itemize}  90  \begin{tabular}{c|c}  Entry 1&amp; Entry 2  \\  Entry 3&amp; Entry 4 \end{tabular}  \end{document}     Also another image of the huge space between two align environments. Even without the blank lines the space is a lot.    \begin{document}  \begin{multicols*}{2}   \begin{align*} &amp;\text{70}\\ &amp;e^{jz}=\cos z+j\sin z\\ &amp;\cos z=(1/2)(2\cos z)=\\ &amp;=(1/2)(2\cos z+j\sin z-j\sin z)=\\ &amp;=(1/2)(\cos z+j\sin z+\cos z-j\sin z)=\\ &amp;=(1/2)(e^{jz}+e^{-jz}) \end{align*}    \begin{align*} &amp;\text{207}\\ &amp;x(t)=A_{c}\cos \theta(t)\\ &amp;\theta(t)=2\pi f_{c}t+\phi(t)\\ &amp;\phi(t)=K_{p}m(t)\\ &amp;x(t)=A_{c}\cos[2\pi f_{c}t+K_{p}m(t)] \end{align*}   Edit I:  As I mention in a comment I have tried the following code and there is no difference between two align environments, only between text and an align environment. Why doesn't work in the case of the two environments and how can I fix it so to work? Also what is the reason that this space exists?  \setlength{\abovedisplayskip}{0pt} \setlength{\belowdisplayskip}{0pt} \setlength{\abovedisplayshortskip}{0pt} \setlength{\belowdisplayshortskip}{0pt} ZF: Difference between POW and SEP? Show that $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$ is linear and continuous Let $k:[0,1]\times[0,1]\rightarrow \mathbb{R}$ continuous and $K:C[0,1]\rightarrow C[0,1]$, given by $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$. Prove that $K$ is continuous. I try to see continuity in $0$, but i can't find $\delta$. From what I've seen it looks to me like Libav's avconv is thought to become a successor of ffmpeg — is that correct?   If that's true, why is that so? What exactly is libav doing better and why would I want to choose it over ffmpeg?   I came to this "issue" while installing Ubuntu 12.04.1 LTS in a VM and when I've installed ffmpeg it came up with a message telling mit ffmpeg is deprecated and I first thought "wtf?".  If I use avconvWill I be able to migrate my scripts depending on ffmpeg more or less easy to libav? I'm mostly using it for writing meta data and doing audio conversion (wav, flac, vorbis, mp3, aac). What diode modifiers are used in practice to model LEDs with SPICE (Berkeley v.3f5)?  are available to me:  #       Name    Parameter                    Units      Default Example  Area 1       IS      Saturation current             A         1e-14   1e-14    * 2       RS      Ohmic resistance               Ω         0       10       * 3       N       Emission coefficient           -         1       1.0 4       TT      Transit-time                   s         0       0.1ns 5       CJO     Zero-bias junction capacitance F         0       2pF      * 6       VJ      Junction potential             V         1       0.6 7       M       Grading coefficient            -         0.5     0.5 8       EG      Activation energy              eV        1.11    1.11 Si                                                                  0.69 Sbd                                                                  0.67 Ge 9       XTI     Saturation-current temperature exponent  3.0     3.0 jn                                                                  2.0 Sbd 10      KF      Flicker noise coefficient      -         0 11    AF      Flicker noise exponent         -         1 12    FC      Coeff. for for.-bias dep. cap. formula   0.5 13    BV      Reverse breakdown voltage      V         ∞       40.0 14    IBV     Current at breakdown voltage   A         1.0e-3 15    TNOM    Parameter measurement temp.    °C        27      50         The dc characteristics of the diode are determined by the parameters IS and N. An ohmic resistance, RS, is included. Charge storage effects are modeled by a transit time, TT, and a nonlinear depletion layer capacitance which is determined by the parameters CJO, VJ, and M. The temperature dependence of the saturation current is defined by the parameters EG, the energy and XTI, the saturation current temperature exponent. The nominal temperature at which these parameters were measured is TNOM, which defaults to the circuit-wide value specified on the .OPTIONS control line. Reverse breakdown is modeled by an exponential increase in the reverse diode current and is determined by the parameters BV and IBV (both of which are positive numbers).   For example, using this basic, cheap red:      I don't care much about high-frequency characteristics -- just would like to be able to match it's IV-curve within its operating specs (-10uA/-5V leakage to +100mA/+2.2'ishV forward): Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?