are there any concrete rules  that say wich words(parts of speech) in a title should start  with a  capital ? what would be a correct capitalization for the title of this question ?
Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question?
Convergence of $A_nT$ to $AT$ in operator norm for compact $T$ $A_n:Y\rightarrow Z$ are operators that strongly converge to $A$. Also, $\|A_n\|_\text {op}\le c$ for $c&gt;0$. Given a compact operator $T:X\rightarrow Y$, I need to show that $A_nT$ converges to $AT$ in operator norm (all spaces in this question are Banach spaces).     I was unable to prove this and I also do not understand why we need to assume that $T$ is compact. Any ideas? Mortarboard badges being awarded as a result of bounties after recalc 50GB of disk space missing On a 120GB SSD hard drive in a MacBook only 70GB are available. The missing 50GB are not even shown as free space.  Here is what the output of Disk Utility looks like:        As you can see on the first screenshot the disk has 120GB. However, the partition chart on the same screenshot only shows 70GB. Also the other two screenshots show that only 70GB out of 120GB seem to be available.  The command diskutil list shows that the physical disk0 is 120GB big, but the synthesized disk1 only 70GB:  /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *121.3 GB   disk0    1:                        EFI EFI                     209.7 MB   disk0s1    2:                 Apple_APFS Container disk1         70.0 GB    disk0s2  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +70.0 GB    disk1                                  Physical Store disk0s2    1:                APFS Volume Macintosh HD            60.2 GB    disk1s1    2:                APFS Volume Preboot                 21.7 MB    disk1s2    3:                APFS Volume Recovery                509.9 MB   disk1s3    4:                APFS Volume VM                      2.1 GB     disk1s4 Should a student be penalized for using a theorem outside of the curriculum? What is the difference between Newtonian and Lagrangian mechanics in a nutshell? What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the explanation of the Lagrangian formulation of mechanics you'd give to someone who just finished a semester of college physics.  Things I'm hoping to have explained to me:   What's the overall difference in layman's terms? From what I've read so far, it sounds like Newtonian mechanics takes a more local "cause-and-effect"/"apply a force, get a reaction" view, while Lagrangian mechanics takes a more global "minimize this quantity" view. Or, to put it more axiomatically, Newtonian mechanics starts with Newton's three laws of motion, while Lagrangian mechanics starts with the Principle of Least Action. How do the approaches differ mathematically/when you're trying to solve a problem? Kind of similar to above, I'm guessing that Newtonian solutions start with drawing a bunch of force vectors, while Lagrangian solutions start with defining some function (calculating the Lagrangian...?) you want to minimize, but I really have no idea. What are the pros/cons of each approach? What questions are more naturally solved in each? For example, I believe Fermat's Principle of Least Time is something that's very naturally explained in Lagrangian mechanics ("minimize the time it takes to get between these two points"), but more difficult to explain in Newtonian mechanics since it requires knowing your endpoint. No sound (speakers/jack) + microphone's dead after spilling water Sadly, yesterday I've spilled some water on my MacBook Pro (El Capitan). Before you yell at me - it was closed, turned off and it wasn't a lot of water, the laptop was wet only on the top and under - not inside.  Today I've turned him on. At first battery wasn't recharging for some reason, but SMC reset fixed the problem.  At the first booting speaker was like talking to me, hard to explain but it was weird. Also only right speaker was "talking", despite the fact that only left side of the laptop was watered. Then there was no sound at all, not from the speakers, nor from the headphones. Also microphone's not working. USB ports are okay. The water was spilled from the left side of the laptop. I know this is hardware issue, and something's broken, but I want to be 100% sure. No it's not muted. I've also tried NVRAM reset a few times, but it doesn't fix the problem :(  There might be one factor, before spilling, my laptop "died" for the first time (battery energy ran off), but I doubt it's the case. (but hey, every info matters, right?)  It wouldn't be weird for me, if only left speaker wouldn't work, but built-in microphone not working is kinda weird in this case, isn't it?  I just want to ask you guys, what else can I check, before I'll be 100% sure it's dead inside?  I've plugged in external microphone - it's not working too. Incorrectly answered 'No' to "Any previous visa refusals..." on a UK Standard Visitor visa application. How can I fix my mistake? I'm from Lebanon and I've been working in Saudi Arabia for nine years. In 2012, I put the money that I collected from my job as a teacher in my father's Lebanese account since I didn't have one in Lebanon. During the interview, my interviewer told me that my application will be rejected because I don't have proof that this money is mine and clearance officer will think someone else gave me the money. I didn't know that I had to bring with me from Saudi Arabia an employment letter and bank statements to prove that this money is mine and I earned it by working in Saudi Arabia. Anyways, my visa did get refused as my interviewer had told me it would be.    Last May, I was granted a US visitor visa Multi Entry for 5 years. I wanted to visit the US in August for 10 days but my mom entered the hospital so I had to postpone it. Now I'm applying for a teacher training program in the UK. I received an invitation letter from Brighton University and so I applied for a UK Standard Visitor visa. After I paid and printed the application, I realized that I answered the question Any previous visa rejections ... with "NO" and I don't know how should I fix this.  Please note that I still didn't give my biometrics, I still didn't use my US visa which I received on May 2016, I paid for my application so I can't amend it online. I'm supposed to give my biometrics and submit my documents this Monday.  If I don't say anything will they check it and refuse me?    Will my US visa be an advantage and they will disregard the previous rejection or should I correct it when I submit my documents this Monday? I used the jQuery Form plugin for asynchronous form submission. For forms that contain files, it copies the form to a hidden iframe, submits it, and copies back the iframe's contents. The problem is that I can't figure out how to find what HTTP status code was returned by the server. For example, if the server returns 404, the data from the iframe will be copied as normal and treated as a regular response.  I've tried poking around in the iframe objects looking for some sort of status_code attribute, but haven't been able to find anything like that.    The $.ajax() function can't be used, because it does not support uploading files. The only way to asynchronously upload files that I know of is using the hidden iframe method. I find that often after awakening from suspend on Ubuntu GNOME 16.04 with GNOME 3.20 (I have only found this issue on the latest version, though I have not tried with GNOME 3.18 on 16.04) that I get this strange font issue which can't be fixed by restarting gnome-shell and seemingly only by restarting my entire machine:            I do not believe that this is a theme issue as I have tried all the built-in themes (including the dark and light versions) and it is the same for them all. Though it does not seem to affect gnome-shell areas, that is the top-bar, the Activities Overview, etc, are not affected for some reason. So what could this issue be caused by and how can I fix or workaround it?  Information Update:  I have had a look at  but the only options in the gnome-tweak-tool for Antialiasing are Rgba, None, and Grayscale, but none of them seem to have any affect on the issue. Is there something I'm missing? How to manipulate a CSV file with sed or awk? How can I do the following to a CSV file using sed or awk?   Delete a column Duplicate a column Move a column   I have a big table with over 200 rows, and I'm not that familiar with sed. I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) How do I efficiently iterate over each entry in a Java Map? Complicated FOR loop nesting. Having trouble cleaning up legacy code How to select kernel for SVM? All rounds of AES (and Rijndael) have a MixColumns step, save the last round which omits it.  DES has a similar feature where the last round differs slightly.  The rationale, if I recall correctly, was to "make the cipher appear similar in reverse as it does in the forward direction."  Why does this make AES$^{-1}$ look similar to AES?  And how does this help in implementing the block cipher? Simple Hadamard Circuit gives incorrect results? How to show full date and time in Nautilus/Files 3.6+ list view? Does a character with 10 Constitution only need to eat every 4 days? According to the food rules,     A character can go without food for a number of days   equal to 3 + his or her Constitution modifier (minimum   1). At the end of each day beyond that limit, a character   automatically suffers one level of exhaustion.   A normal day of eating resets the count of days   without food to zero.   According to this, a character with a Constitution modifier of 0 can eat normally every 4th day*, and get no penalties from hunger despite only eating twice a week. This seems a tad ridiculous, and I'm wondering if there are other rules that I'm missing that make it a bad idea to eat less often like this, or if eating every 4th day is a totally fine thing to do, by the rules.  * They can get away with four days, because they'll only get the exhaustion penalty if they don't eat by the end of the fourth. This is even assuming the 'minimum 1' doesn't apply to the con mod portion. How to group distinct values from a list using odata rest api Compound possessives and yours