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t-test for partially paired and partially unpaired data Are these gerund sentences grammatically correct? I bought this book titled 2 Hari Taklukan Grammar, written by Edward Rahardian in Bahasa (Indonesian language) and mostly talk about gerund and infinitive. And these are some examples of the gerund sentences that I found.        His mother suggested having lunch before we leave.     I will try studying harder.     The car needs washing.     Your hair needs washing.     My teacher disliked me coming late.        Somehow those words sound unnatural for me because I've never heard those in daily conversations. As a learner, I only get exposed with English by watching TV series and any other entertainment resources.  So in my thought, they sound more natural like this:        His mother suggested to have lunch before we leave.     I will try to study harder.     The car needs to be washed.     Your hair needs to be washed.     My teacher disliked me to come late.       Are those sentences in the first group grammatically correct? And, is it normal for one to say them in normal/daily conversations? There are so many questions on this website. There is so many questions on this website.  The former &quot;sounds right,&quot; but the contracted form of the latter does as well:  There's so many questions on this website.  Which is correct? I'm trying to install Ubuntu 12.10 alongside Windows 7 on my ASUS laptop and I'm new to all of this.   I'm using  the Ubuntu 12.10 64-bit ISO burned onto a CD.  The first time I tried to install it, Ubuntu said it did not detect any other OS, which meant I only had 4 options:   Erase disk and install Ubuntu (I don't want to do this) Encrypt new Ubuntu. Use LVM. Something else.   If I choose the Something else option, it brings me to the partition menu and says that I have 1 disk with free space of 750516Mb (750Gb), but that's not true because I have Windows 7.  I've already read through several questions and people have mentioned that you could only have 4 primary partitions. So I got hold of partition magic and removed my D: and E:, leaving me with primary C: partition and System reserved partition and a lot of unallocated space.  I restarted the laptop several times and booted the CD again and I got exactly the same as I did previously.  How do fix this problem and install Ubuntu alongside Windows 7?  EDIT 1  Here are my results for   sudo fdisk -l; echo; sudo parted -l; echo; mount; echo; df -h   WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 750.2 GB, 750156374016 bytes 255 heads, 63 sectors/track, 91201 cylinders, total 1465149168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x90050371     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048      206847      102400    7  HPFS/NTFS/exFAT /dev/sda2          206848   146368214    73080683+   7  HPFS/NTFS/exFAT  Warning: /dev/sda contains GPT signatures, indicating that it has a GPT table. However, it does not have a valid fake msdos partition table, as it should. Perhaps it was corrupted -- possibly by a program that doesn't understand GPT partition tables.  Or perhaps you deleted the GPT table, and are now using an msdos partition table.  Is this a GPT partition table? Yes/No?     After selecting YES  Yes/No? yes                                                                Error: The backup GPT table is corrupt, but the primary appears OK, so that will be used. OK/Cancel? PostgreSQL multi-column unique constraint and NULL values I have a table like the following:  create table my_table (     id   int8 not null,     id_A int8 not null,     id_B int8 not null,     id_C int8 null,     constraint pk_my_table primary key (id),     constraint u_constrainte unique (id_A, id_B, id_C) );   And I want (id_A, id_B, id_C) to be distinct in any situation. So the following two inserts must result in an error:  INSERT INTO my_table VALUES (1, 1, 2, NULL); INSERT INTO my_table VALUES (2, 1, 2, NULL);   But it doesn't behave as expected because according to the documentation, two NULL values are not compared to each other, so both inserts pass without error.  How can I guarantee my unique constraint even if id_C can be NULL in this case? Actually, the real question is: can I guarantee this kind of uniqueness in "pure sql" or do I have to implement it on a higher level (java in my case)? I can see by manipulating the expression why $\mathbb{E}X$ works out to be $\int_0^\infty 1-F(x)\,dx$, where $F$ is the distribution function of $X$, but what is an intuitive explanation for why that is true? If at each point we sum the probability $\mathbb{P}(X&gt;x)$, why should we end up with the expectation?  Thanks What measures can/should I take to make sure that security around my SSH server is absolutely impermeable?  This will be community wiki from the start, so lets see what people do to secure their servers. How to select top 10 records from each category Why, logically, is proof by contradiction valid? $\mathbb S_n$ as semidirect product In  note, I've read that $\mathbb S_n$ is a semidirect product of the alternating group $A_n$ by $\mathbb Z_2$. So I am trying to define a morphism $\rho: \mathbb Z_2 \to Aut(A_n)$ to show that $\mathbb S_n \cong A_n \rtimes Z_2$. I would appreciate suggestions on how could I define the morphism. Thanks in advance. What really causes light/photons to appear slower in media? I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm interested in - I want to go deeper than that. We know that the real speed of light is actually not changing, the decrease in speed is just apparent. Material is mostly empty, the light will still travel with $c$ in the spacing. The rare atoms will disturb the light in some way. So I am interested in how the atoms affect the light. Photon absorption-emission theory Some textbooks that I read explain it in a way kind of like this: In a material the photons are absorbed by atom and then re-emitted a short time later, then they travel a short distance to the next atom and get absorbed&amp;emitted again and so on. How quickly the atoms in a material can absorb and re-emit the photon and how dense the atoms decides the apparent speed of light in that material. So the light appears slower because it has a smaller “drift speed”. Interference theory But recently I realize an alternative explanation: Atoms respond to the light by radiating electromagnetic wave. This “new light” interferes with the “old light” in some way that results in delayed light (advanced in phase), this can easily be shown by using simple phasor diagram. Consequently effectively the light covers a smaller phase each second, which gives the impression of a lower phase velocity. However the group velocity is changing in a complicated way. I think that the first explanation does not explain the change in phase velocity of light. if we consider light travelling into a slab of negative refractive index non-dispersive material, let’s say the light is directed perpendicular to the slab. The phase velocity’s direction will be flipped, but group velocity’s direction in the material will not change. Only the second explanation can explain the flipped phase velocity direction. I guess that the velocity that we get in the first explanation is actually belongs to the group velocity. It makes sense to me that the front most of the photon stream determines the first information that the light delivers. So the question is What really cause the phase velocity of light to be decreased?  &quot;drift velocity&quot; of photons (they aren't the same photons, they are re-emitted all the time) phase difference between absorbed and emitted light something else  And also, I still don't really understand detailed explanation of the absorption-emission process for small light's wavelength (for large lambda compare to the atoms spacing, the photons will be absorbed by the phonons). The dispersion relation that we know is continuous and also some material is non-dispersive, therefore the absorption process must occur in all frequency for a certain range. So definitely it doesn't involve the atomic transition, otherwise it will be quantized. My guess is that the relevant absorption process gets smooth out by the dipole moment. What makes the spectrum continuous? EDIT: link for dispersion relation: How can I correct a reviewer's opinion? Why do my xmodmap binds involving AltGr only work on some keys? I want to remap my AltGR+Right_Windows but I can't figure out how. No matter what I try, pressing the right windows key emits the name keysym when right alt is pressed or not.  These are the contents of the xmodmap file I am testing right now. In my keyboard, 38 is the keycode for "a", 48 is the keycode for aportrophe/doublequote and 134 is the keycode for the right windows key.  keycode  38 = 1 2 3 4 5 6 7 8 keycode  48 = 1 2 3 4 5 6 7 8 keycode 134 = 1 2 3 4 5 6 7 8   When I press Right_Alt+apostrophe, it outputs 5 but Right_Alt+a and Right_Alt+Right_Windows give 1 (both when right alt is pressed and when it isn't) which is not what I wanted.  My current keyboard layout is us(alt-intl) and the right alt is apparently set up to act as AltGr / Iso_Level3_Shift. The output of xmodmap -pm is the following:  xmodmap:  up to 4 keys per modifier, (keycodes in parentheses):  shift       Shift_L (0x32),  Shift_R (0x3e) lock        Caps_Lock (0x42) control     Control_L (0x25),  Control_R (0x69) mod1        Alt_L (0x40),  Meta_L (0xcd) mod2        Num_Lock (0x4d) mod3       mod4        Super_L (0x85),  Super_R (0x86),  Super_L (0xce),  Hyper_L (0xcf) mod5        ISO_Level3_Shift (0x5c),  Mode_switch (0xcb) Unexpected output of xargs Can anyone please help and tell me if this sentence is correct?  &quot;A significant amount of zombies were detected in your city.&quot;  In my opinion it should be &quot;A significant amount of zombies was detected in your city.&quot; because &quot;amount&quot; should be in agreement with &quot;was&quot; even though amount usually refers to something plural. Are both (was and were) acceptable in this case? Edit1: Yes, &quot;number&quot; would be the correct one in this case. So allow me to ask one more thing.  &quot;A significant amount of purchases were detected...&quot;  Does the use of &quot;number&quot; apply in this case also? As purchase is not exactly a thing/person. And if no, is it correct to say &quot;A significant amount of purchases were detected...&quot;? Edit2: So, please tell me what is the correct phrasing?  &quot;A significant amount of purchases were detected...&quot; &quot;A significant amount of purchases was detected...&quot;  Or, since purchases are countable, is the use of &quot;number&quot; instead of &quot;amount&quot; correct here, as in:  &quot;A significant number of purchases were detected...&quot; &quot;A significant number of purchases was detected...&quot;  Or would amount be correct since a purchase involves money and it refers to the amount of money? Would greatly appreciate an answer, and if possible a detailed explanation. Is there any other way to do a clean install withot formatting /home? I think my Ubuntu is a bit broken from messing around with it.  Unfortunately during installation, I did not make a separate partition for /home. Now I need to re-install but want to keep my music and films.  Any ideas... We want to find the solution $x$ to the congruence system  $$\begin{align} x &amp;\equiv r_1 \!\!\!\pmod{\!m_1}\\ x &amp;\equiv r_2 \!\!\!\pmod{\!m_2}\end{align},\ \ {\rm where}\ \  \gcd(m_1, m_2) = 1$$  These can be rewritten as  $$\begin{align} x &amp;= r_1 + m_1 j\\ x &amp;= r_2 - m_2k\end{align}$$  for unknown integers $j, k$. So we set those two equations as equal and rearrange them to  $$m_1j + m_2k = r_2 - r_1$$  Now assume we perform $\text{egcd}(m_1, m_2)$, which gives us the solution to  $$m_1u + m_2v = \gcd(m_1, m_2)$$  Let the integer $\,h\,$ make $\,h \gcd(m_1, m_2) = r_2 - r_1$.  Then $\qquad hm_1u + hm_2v = h\gcd(m_1, m_2) =  r_2 - r_1 = m_1j + m_2k$  At this point I am lost because I don't think we can just assume  $hm_1u = m_1j$ and extract $j = hu$.   How do I get the values of $j$ or $k$ so I can get the value of $x$? I’ve always understood that the phrase two weeks usually turns into two weeks’ when used as a modifier as in   I’m giving my two weeks’ notice.  I get two weeks’ vacation. (“two weeks’ holiday” for Brits)   with an apostrophe on the word weeks’, indicating that the vacation “belongs” to the weeks.   One way to explain this is the phrase “two weeks of vacation” being contracted to “two weeks’ vacation” – the vacation is “of” the weeks; that is, it is possessed by them.  But I’ve seen a lot of people omit the apostrophe in casual writing, and thinking about it, it seems plausible that the noun vacation would be plainly modified by the adjectival phrase two weeks.  But on the other hand, shouldn’t adjectival phrases be hypenated, namely two-weeks vacation?  Yet that seems wrong, too: the hyphenate should be singular, two-week vacation (like two-tone shoes) because .   touches on this (and references a good ) but doesn’t explain why the plural must be possessive in this case.   suggests that two weeks might be adverbial rather than adjectival, and thus resists being used attributively. But that still doesn’t quite explain this particular muddle of pluralization, possession, and attribution.  Given all this, why should “two weeks vacation” be written “two weeks’ vacation” with a possessive apostrophe? I am a new user of Ubuntu 12.04.   I installed Ubuntu and Windows XP, and I want to use both operating systems. When I restart or boot my PC the GRUB menu does not appear.  How can I solve this problem? What to do with an Ubuntu disk image that appears as a WinRAR file?