Physical meaning of Laplace Transform
Creating intuition about Laplace & Fourier transforms
"When I grow up, I am going to be a doctor"- Is it correct? When I grow up, I am going to be a doctor.   Is this sentence correct? Personally I think my growing up will happen in future and "I am going to be a doctor" sounds like it is going to happen in next month! But the sentence clearly indicates the speaker is a child. So according to me, "I am going to be a doctor" should be replaced by "I will be a doctor". So I think a more clear sentence would be     When I will grow up, I will be a doctor.   Is my concept correct here? I use ssh on a variety of machines, mainly linux. Accounts on these machines vary in naming scheme: if my name is First Last, then I have accounts: first, flast, last_f, lastf, and sometimes I need to log in as root. For each machine I use, I would like the openssh client to know which account to use when I don't specify on the command line.  So the question is: How do I make ssh server Do The Right Thing when a username is not specified? Implementing a sort of "tightened frenchspacing" By default, (La)TeX adds extra space between sentences. The exact rules are in the TeXbook, a summary by TH. can be found . What follows is is my "executive summary":   After any period (or quotation/exclamation mark) that doesn't follow a capital letter, TeX adds a font's "extra space" to the "normal (interword) space". For Computer Modern 10pt, the normal space is 3.33pt and the extra space 1.11pt, resulting in an intersentence space of 4.44pt (+33% compared to the nomal space, assuming no stretch and shrink). A sentence end after a capital letter is indicated by the \@ command: Ann is learning the ABC\@. To denote that a period after a lowercase letter doesn't end a sentence, one may use \@ as well as an explicit space: Prof.\@ Higgins or Prof.\ Higgins.   Intersentence spacing may be brought in line with normal spacing by issuing the \frenchspacing command. (This is the standard setting for certain languages, e.g. the  (n)german option of the babel package.) With \frenchspacing enabled, there's no need to use the \@ command. One may revert to (La)TeX's default behavour by issuing \nonfrenchspacing.  So, there's the choice between extra intersentence spacing and uniform spacing. What is missing in my opinion is a third option I'll call "tightened frenchspacing": normal (interword) spacing between sentences and decreased spacing after non-sentence ending periods. To be somewhat more precise (while still ignoring stretch and shrink), I envision the following:   Adhering to a font's ratio between "normal space" and "normal space plus extra space" (3:4 for Computer Modern), the intersentence space is set to the normal space. The space after non-sentence ending periods equals the normal space multiplied by the above ratio (resulting in a space of 2.5pt for Computer Modern). As with \nonfrenchspacing in effect, the \@ command is used to denote cases of special punctuation.   How should such a "tightened frenchspacing" option be implemented?  EDIT: Thanks to Mico for providing what may well be a stepping stone to a solution. Here's another attempt at clarification:   Simply reducing the spacing after any period is not what I had in mind. There should be a (tangible) difference between end-of sentence spaces and spaces after non-sentence-ending periods (only that the latter should be reduced instead the former augmented). If adhering to a font's normal space/extra space ratio is not possible, a solution that adds a fixed (reduced) space (say, a thin space) after non-sentence-ending periods will be accepted. For compatibility reasons, I'd prefer a solution that works with the traditional use of \@ (i.e allows "tightened frenchspacing" for existing documents without the need to change the document body). Should it turn out that a different set of "special punctuation" macros is needed, I'll accept this as a solution. How to display citations in text grouped as [1-3] in stead of [1,2,3] I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct? I use pgfplots for most of my plots. Now I need to add a . Is this possible with pgfplots or any other package? Atmospheric pressure In FBD doubt Let us say I have a beaker floating in a water tank. Suddenly I put some water in the beaker also. The figure here shows the exact situation   Now I want to draw the FBD of the beaker. I am somehow confused with the role of the atmospheric pressure in drawing the FBD. I thought of two ways of drawing this and I am just unable to figure out which one is right.    Here since the beaker is floating an $F_{buoyant}$ is there in the upward direction which the net mass (beaker+water in beaker) would put its weight downward.  But while solving one question I came to know that total force that a liquid exerts on the bottom of the container is $P_0+m_{liquid}g$ ($P_0$ is the atmospheric pressure). So should the downward force on the beaker be $(M_{beaker}+M_{water in beaker})g+P_0 S$ (S being the base area of the beaker) as in the second diagram down here.    Here the $P_0S$ due to atmospher on the tube gets cancelled by the $P_0S$ exerted by the water in tank on the tube. But what about the $P_0S$ from the water present in the tube? Do the FBD's apply like the one in the new image? How to prove reflexivity, symmetry and transitivity for the following relation? Does 'but for' mean:  'If we had X (but we didn't), Y would have been the consequence'?  Or can it also mean; because we had X, as a result Y happened?   Some different examples of but for:  (Case 1)     But for a cup coffee, it was to be a productive day of writing.   Unfortunately, I'd run out, and spent the day craving.    (Case 2)     But for the glass of wine I had dinner, the house work didn't get   done.   (Case 3)     But for the glass of wine I had for dinner, I would have got the   house work done   What is the correct usage of "but for"? How do I read a text file with variable hexadecimal value columns in matlab? only display df lines that have more fs usage than 80% root@SERVER ~$ df Filesystem  512-blocks  Free    %Used   Iused   %Iused  Mounted on /dev/YXCV   655360      365632  45% 6322    13% / /dev/ASDF   3801088     670648  83% 41759   32% /usr /dev/ASR    1048576     500496  53% 5555    9%  /var   How can I pipe the df command's output to only display lines that have more usage than 80%?  e.g.: it would only display:  /dev/ASDF   3801088     670648  83% 41759   32% /usr Press space to continue How do I stop a bash script until a user has pressed Space?  I would like to have the question in my script     Press space to continue or CTRL+C to exit   and then the script should stop and wait until Space is pressed. Take a look at this example schematic:  The chip in question is the  and as you can see power is provided on both sides (with a 100nF cap to smooth noise I guess). Is this strictly required or could you put power into one side and just ignore the other? I know that I have just put power in one side and everything still seems to work fine but I feel uneasy with doing that. I feel that they would not waste pins that could be doing something useful by having an extra pair of power in/out pins. For what purpose does this PIC MCU (and others like it) have multiple power pins? So if I'm correct, when you chose your starter gear and wealth you can either choose to roll some dice depending on your class and buy everything from that or you can choose the starter gear from your class and add the background items (including some gold). Here are my 2 questions:   If I choose the gear from my class, do I have to take all the equipment from only one of the (a) or (b) choices, or can I freely mix-and-match choices from the two sets? Can you spend the extra gold you get from your background on extra equipment (e.g. some soap and some fishing equipment) or do you have to start with that gold in its pouch?   The reason I ask is that I have recently created a level 1 wood elf druid and I mixed-and-matched the gear from the class, so that I chose a shortbow as a "(b) simple weapon" for the first point and a "(a) Scimitar" at the second point. My DM wasn't so happy about this, as he can't understand why I'm mixing (a) and (b).  He also wasn't so happy with me spending my 10gp from my outlander background. I decided that my druid wouldn't lay so much worth in 10gp compared to a bunch of stuff I got for that (e.g. some soap and some fishing equipment and some other useful things) and he seems to think that I'm supposed to just start with the gold instead. Proving $\sum_{k=0}^n(-1)^k\binom nk=0$ When is "seems to be" used instead of "seems"? The baby seems happy/comfortable. The baby seems to be happy/comfortable.   Are these both correct? If both are correct, what are the differences between them? Ubuntu equivalent of system restore? Does it exist? Ubuntu n00b here.  I have created several disasters of the first order already.  I am getting ready to try to install opera - it is a very long and arduous process.  I am afraid - no - I am absolutely certain that I will damage something important.  How do I create a system restore point?  Does such a thing exist? so i change my MAC address with macchanger -A wlp68s0b1 at boot with crontab, here is what happens when i disconnect and reconnect :  while connecting after boot :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:22:31:c6:38:45 (SMT&amp;C Co., Ltd.) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after disconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   16:7b:e7:3c:d3:cd (unknown) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   after reconnecting :  rahman@debian:~$ macchanger -s wlp68s0b1 Current MAC:   00:00:00:00:00:00 (FAKE CORPORATION) Permanent MAC: 00:00:00:00:00:00 (FAKE CORPORATION)   and so on, and with every disconnect i get a different random MAC address which fades on reconnecting giving me my real MAC address , what causes that and how to stop it ?  some outputs :  rahman@debian:~$ lspci -nn |grep 14e4 44:00.0 Network controller [0280]: Broadcom Limited BCM4313 802.11bgn Wireless Network Adapter [14e4:4727] (rev 01) rahman@debian:~$ uname -a Linux debian 4.9.0-3-amd64 #1 SMP Debian 4.9.30-2+deb9u5 (2017-09-19) x86_64 GNU/Linux rahman@debian:~$ sudo ifconfig  enp0s25: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         RX packets 0  bytes 0 (0.0 B)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 0  bytes 0 (0.0 B)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0         device interrupt 20  memory 0xd4800000-d4820000    enp0s25:avahi: flags=4099&lt;UP,BROADCAST,MULTICAST&gt;  mtu 1500         inet 169.254.9.109  netmask 255.255.0.0  broadcast 169.254.255.255         ether 00:24:c0:7b:a8:8b  txqueuelen 1000  (Ethernet)         device interrupt 20  memory 0xd4800000-d4820000    lo: flags=73&lt;UP,LOOPBACK,RUNNING&gt;  mtu 65536         inet 127.0.0.1  netmask 255.0.0.0         inet6 ::1  prefixlen 128  scopeid 0x10&lt;host&gt;         loop  txqueuelen 1  (Local Loopback)         RX packets 9436  bytes 6584515 (6.2 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 9436  bytes 6584515 (6.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  wlp68s0b1: flags=4163&lt;UP,BROADCAST,RUNNING,MULTICAST&gt;  mtu 1500         inet 192.168.1.5  netmask 255.255.255.0  broadcast 192.168.1.255         inet6 fe80::6711:9875:eb78:24fc  prefixlen 64  scopeid 0x20&lt;link&gt;         inet6 fd9c:c172:b03b:ce00:f1e0:695e:7da0:91a  prefixlen 64  scopeid 0x0&lt;global&gt;         ether 00:00:00:00:00:00  txqueuelen 1000  (Ethernet)         RX packets 484346  bytes 641850809 (612.1 MiB)         RX errors 0  dropped 0  overruns 0  frame 0         TX packets 368394  bytes 44259668 (42.2 MiB)         TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0  rahman@debian:~$ sudo iwconfig  lo        no wireless extensions.  enp0s25   no wireless extensions.  wlp68s0b1  IEEE 802.11  ESSID:"3bdo"             Mode:Managed  Frequency:2.447 GHz  Access Point: 9C:C1:72:B0:3B:D4              Bit Rate=65 Mb/s   Tx-Power=30 dBm              Retry short limit:7   RTS thr:off   Fragment thr:off           Encryption key:off           Power Management:off           Link Quality=54/70  Signal level=-56 dBm             Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0           Tx excessive retries:4  Invalid misc:183   Missed beacon:0 Can the system leave a deletion reason when it deletes a question? How to test if my server is vulnerable to the ShellShock bug? How can I ensure my Bash installation is not vulnerable to the  bug anymore after the updates?