I only know "towards" and always use it before today: "move towards", etc. But today, I come across toward, after referring the dictionary, I find I can't differentiate them clearly. What is the difference between "toward" and "towards"? How can use them?
Which one should should I use? For some reason I have always used "towards", but I see some people saying "toward", like :     A great deal of his work in economic   theory has been directed toward   strengthening the foundations of our   understanding of central banking and   social insurance--indeed, one of my   most advanced macroeconomic classes   was nothing but a set of changes rung   upon a particular model that Peter   Diamond had advanced at...   Is there a difference between the two? When should they be used?
Is there a drupal.org API for retrieving the list of available modules, a description of them and available versions? Is Gauss's law wrong, or is it possible that $\int_s{\vec E} \cdot d\vec{s}=0$ does not imply $\vec E = 0$? This is a question from David J Griffith's Introduction to Electrodynamics.      A specified charge density $\sigma(\theta)=k\cos(\theta) $ is glued over the surface of a spherical shell of radius $R$. Find the resulting potential inside and outside the sphere.   The question was solved using legendre polynomials and the final answer for potential inside the sphere was : $V(r,\theta) = \frac{kr}{3\epsilon_0}cos\theta$  This final answer is confusing because The Electric field inside the sphere is coming out to be dependent on $r$ and $\theta$ whereas electric field inside a shell, no matter what the charge distribution is outside, is $zero$ from gauss's law.      my doubts:         why is the electric field inside non zero?    Can gauss's law explain this, or does it fail here?      Since solving using ordinary surface integral gave me the same result and since the. divergence inside the shell is $zero$, I concluded that legendre polynomials and gauss's law in differential form are correct. So the problem should be with the integral form of gauss's law : $\int_s{\vec E}.d\vec{s} = \frac{q}{\epsilon_0}$  The answer I got for this doubt is that  "since the charges are glued to the surface, and not evenly distributed, electric field inside need not be zero. "     This is not convincing because proof of gauss's law does not expect the charges to be free to move. presence of an exrernal force that would hold the charges in place does not change the theorem. That is    Say only a single charge $q_i$ is present outside      then $\int_s{\vec E_i}.d\vec{s} = \frac{q_{inside}}{\epsilon_0}=0$      Now if there are more charges, following any distribution, net electric field $\vec E = \vec E_1 + \vec E_2+\vec E_3+...$       So the net flux,       $\int_s{\vec E}.d\vec{s} = \int_s{\vec E_1}.d\vec{s}+\int_s{\vec E_2}.d\vec{s}+\int_s{\vec E_3}.d\vec{s}+. . .=0$   Or is it possible that $\int_s{\vec E}.d\vec{s}=0$ does not imply $\vec E = 0$? Why didn't the Ministry use Veritaserum to question criminals? The truth potion (Veritaserum) is one of the most powerful potions that forces the drinker to speak truth. Then why didn't Ministry used it in any criminal cases instead of long discussions and proceedings? I know there are antidotes to the potion (Dumbledore tells Harry in the 6th book , "Slughorn might have been carrying antidote to veritaserum ever since I asked him about the memory"), but why don't keep criminals in custody until the effect of the antidote wears out and then make them drink veritaserum. Won't that result in perfect judgement? Is it acceptable to publish a paper using an affiliation with a former employer? Recently I've changed jobs, and consequently the field of research has also changed. But I'm still getting proposals for publications in the previous field, and it is interesting for me to accept some of them. My concern is about which affiliation to use: on one hand I gain all the knowledge in that field while working on the previous employer, also I hope they can cover my expenses related to the publication. On the other hand, I do not work for them anymore, and my current company has very little interest in my old field of research, and probably will not support it financially, but I think it is wise to mention them as well. As a compromise I'm thinking to put the previous employer in the affiliation, and the name of my new employer in the footnote, something like "currently at XYZ". Surely I'll discuss this issue with both, although the opinion of the community is also very valuable. Can a Raspberry Pi run Ubuntu? I was thinking about buying a , and running Ubuntu on it. I have looked around the web, and a lot of stuff says that it's difficult for it to work on ARM processors. Has anyone figured out how to get a Raspberry pi to run Ubuntu? Find the population size that maximizes the probability that two random samples of size $20$ will have exactly $2$ members in common Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked.  (a) Find the probability of 2 of the 20 fish being marked if the lake has $k$ fish (assuming the fish are caught at random). (b) What value of k maximizes the probability?    Progress:     I got the (a), $$\binom{10}{2}\binom{k-10}{18}\bigg/ \binom{k}{20}$$ But how do I get part (b) where $k$ is to maximize the probability? I'm runing 15.04 on a dell xps 13 bluetooth recognises devices when i  try to add them but won't let me connect to them Here is the results from my terminal.  ~ $ uname -a; lspci -nnk | grep -iA2 net; lsusb; dmesg | grep -i bluetooth; dmesg | grep -i firmware; lsmod | grep bluetooth  Linux aaron-XPS-13 3.19.0-15-generic #15-Ubuntu SMP Thu Apr 16 23:32:37 UTC 2015 x86_64 x86_64 x86_64 GNU/Linux 02:00.0 Network controller [0280]: Broadcom Corporation BCM4352 802.11ac Wireless Network Adapter [14e4:43b1] (rev 03)     Subsystem: Dell Device [1028:0019]     Kernel driver in use: wl Bus 003 Device 002: ID 8087:8001 Intel Corp.  Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 0bda:5682 Realtek Semiconductor Corp.  Bus 001 Device 002: ID 0a5c:216f Broadcom Corp.  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub [    8.164048] Bluetooth: Core ver 2.20 [    8.164065] Bluetooth: HCI device and connection manager initialized [    8.164069] Bluetooth: HCI socket layer initialized [    8.164073] Bluetooth: L2CAP socket layer initialized [    8.164079] Bluetooth: SCO socket layer initialized [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [    8.353166] Bluetooth: hci0: BCM: patch brcm/BCM20702A0-0a5c-216f.hcd not found [   20.289452] Bluetooth: BNEP (Ethernet Emulation) ver 1.3 [   20.289455] Bluetooth: BNEP filters: protocol multicast [   20.289459] Bluetooth: BNEP socket layer initialized [   20.310897] Bluetooth: RFCOMM TTY layer initialized [   20.310907] Bluetooth: RFCOMM socket layer initialized [   20.310912] Bluetooth: RFCOMM ver 1.11 [  886.399085] Bluetooth: hci0 urb ffff8800d8c15e40 failed to resubmit (2) [  895.471190] Bluetooth: hci0: BCM: patching hci_ver=06 hci_rev=1000 lmp_ver=06 lmp_subver=220e [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e [    8.353160] bluetooth hci0: Direct firmware load for brcm/BCM20702A0-0a5c-216f.hcd failed with error -2 [  896.113983] Bluetooth: hci0: BCM: firmware hci_ver=06 hci_rev=1624 lmp_ver=06 lmp_subver=220e bluetooth             491520  22 bnep,btusb,rfcomm ~ $ Transforming positively skewed data with positive and negative values My data (see image below) is positively skewed and contains both positive and negative values. I'd like to transform it to achieve normality so I can apply a repeated measures ANOVA, but can't find a technique that works.  I've considered the following options:   Square-rooting: doesn't keep the sign Square-rooting then making the original negative values negative: makes my data bimodal Natural log transform: can't do this with negative values Add a constant then log transform: this arbitrarily leaves my lowest value as an outlier '' transform (Cox, 2005; also Whittaker et al. 2005): makes my data bimodal Outlier removal (2.5 SD): doesn't fix normality, but an ANOVA on this data has similar results to an ANOVA on the raw data (for better or worse). Perform the non-parametric equivalent (Friedman test) and compare the results: will do this today   My supervisor suggests I should stick with the outlier removal though the data is still visibly skewed, and 'see what the reviewers suggest' but I just wanted to check here in case there was anything I was missing.  Original data:    With outliers (2.5 SD) replaced with the value at that criterion. I later decided to just exclude the outliers, so imagine the highlight data points in each condition removed. Suppose that $X_1,X_2,...,X_n$ is a random sample from a normal distribution, $X_i\sim N(\mu,9)$.  Find the UMVUE (uniformly minimum variance unbiased estimator) of $P(X\le c)$ where $c$ is a known constant.  Do this by finding the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$ and apply the Rao-Blackwell theorem with $T=u(X_1)$, where $u(x_1)=1$ if $x\le c$ and zero otherwise.  So clearly the parameter that we're trying to estimate given the problem description can be written as $\Phi\left( \frac{c-\mu}{3} \right)$ where $\Phi$ represents the CDF of the standard normal distribution.  However, I get stuck when I need to try and find the conditional distribution.  Without knowing the joint distribution or the other conditional distribution, how can I possibly find the conditional distribution of $X_1$ given $\bar{X}={\bar{x}}$? Deciphering the .NET clr20r3 exception parameters P1..P10 Understanding QGIS buffer tool units I  have had no luck getting the buffer tool to accept anything but degrees as units of measure.  I have found lots of stuff saying the layer needs to be reprojected and saved but it hasn't worked at all for me.   Is there a way I could create a buffer without using ftools or at least force the units to meters somehow?  As a workaround I converted meters to degrees (lat) and used that but the final product needs to be as close to reality as possible.  Things I've tried:   setting every unit option I could find to meters (where possible). setting everything to NAD83/Maryland (data is for Washington, DC) and saving it as such (as layers in ESRI shape files). reimporting the reprojected layers setting relevant layers to Google Mercator   The was tried followed by creating a buffer. Many were tried in combination. QGIS 1.7.3 Slackware64 current (qgis from SBo-13.37 repo, tried on multilib and plain 64it with same results) How can I copy from Tmux terminal and paste it other application in my OS? I am using tmux on ubuntu. I read this  for copy and paste inside tmux. But I would like to know how can I copy from TMUX terminal and paste it to other application e.g browser in my OS? My laptop (running Win10) repeatedly "steals" the bluetooth connection for my headphones while they're connected to my phone. The only way I've been able to prevent the headphones' connection from switching to the laptop is to play some media or make a phone call immediately after reconnecting to my phone, or to unpair the headphones from the laptop.  The headphones are Plantronics Backbeat Go 2, and the specifications from the Plantronics product page give the following information for the Bluetooth entry:      Bluetooth v2.1:   A2DP 1.2, AVRCP, HFP v1.5, HSP v1.1   Thanks in advance! Is there a difference between foo(void) and foo() in C++ or C? Consider these two function definitions:  void foo() { }  void foo(void) { }   Is there any difference between these two? If not, why is the void argument there? Aesthetic reasons? Is it OK to reduce the charging current for a Li-ion 18650 battery? I am using NCR18650 batteries with the tp4056 charging module.  When I connect the charger at 2.8&nbsp;V (fully discharged), the tp4056 IC is getting hot at a 1&nbsp;A charge current. Is it OK to reduce this charge current by changing the charge current selecting resistor? So the tp4056 IC heat would be reduced, wouldn't it?  For my application I don't need a quick charge. With a low current, charging time will be increased, but it does not matter for my application.  Will reducing the charge current affect the battery's lifetime? Or will it damage the battery?  I am trying to reduce the heat of the tp4056 IC by reducing the charging current, maybe from 1&nbsp;A to 500&nbsp;mA or less. The 18650 battery never heats for a 1&nbsp;A charge current. If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$? If I have a manifold $M$ and $\omega \in \Omega^q(M)$, considered an open subset $U$ of $M$, and choose a point $p \in M$, is it true that $(\omega|_{U})_p=0 \rightarrow \omega_p=0$? With $\omega|_{U}$ I mean the pull-back of $\omega$ by the embedding $F:U\to M$. The converse is obviously true, but this implication? I have a script that I need to execute on an NTFS partition. The script's permission is set to 600.  I attempted to modify the permissions by running chmod 755 script.sh, which doesn't report a failure or anything - but it also doesn't change the permissions on the file:  $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700  $ chmod 755 script.sh $ stat script.sh    File: `script.sh'   Size: 297070      Blocks: 584        IO Block: 4096   regular file Device: 811h/2065d  Inode: 35515       Links: 1 Access: (0600/-rw-------)  Uid: ( 1000/  xxxxxx)   Gid: ( 1000/  xxxxxx) Access: 2010-09-30 14:05:16.041621000 -0700 Modify: 2010-09-30 14:05:05.070157000 -0700 Change: 2010-09-30 14:05:05.070475000 -0700   As you can see, it remains unchanged. The definition for marker below is from tcolorbox.doc.s_main.sty. With earlier versions of Texlive (and tcolorbox), this worked fine, but with updated Texlive, it does not.  \documentclass{article} \usepackage{xcolor,tikz,tcolorbox} \usetikzlibrary{shadows} \tcbuselibrary{skins,hooks} \makeatletter % from tcolorbox.doc.s_main.sty \newtcolorbox{marker}[1][]{enhanced,   before skip=2mm,after skip=3mm,   boxrule=0.4pt,left=5mm,right=2mm,top=1mm,bottom=1mm,   colback=yellow!50,   colframe=yellow!20!black,   sharp corners,rounded corners=southeast,arc is angular,arc=3mm,   underlay={%     \path[fill=tcbcol@back!80!black] ([yshift=3mm]interior.south east)--++(-0.4,-0.1)--++(0.1,-0.2);     \path[draw=tcbcol@frame,shorten &lt;=-0.05mm,shorten &gt;=-0.05mm] ([yshift=3mm]interior.south east)--++(-0.4,-0.1)--++(0.1,-0.2);     \path[fill=yellow!50!black,draw=none] (interior.south west) rectangle node[white]{\Huge\bfseries !} ([xshift=4mm]interior.north west);     },   drop fuzzy shadow,#1} \makeatother   \begin{document} \begin{marker}   Hylo! \end{marker}  \end{document}   This gives the following error  ! Package xcolor Error: Undefined color `tcbcol@back'.  See the xcolor package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.34 \end{marker}  ?   Why are tcbcol@back and tcbcol@frame undefined if they work in the code for the package's documentation? Alternatively, what are the correct names for the colours which were tcbcol@back and tcbcol@frame?  My version of tcolorbox is 2019-09-19. I have an HTML string representing an element: '&lt;li&gt;text&lt;/li&gt;'. I'd like to append it to an element in the DOM (a ul in my case). How can I do this with Prototype or with DOM methods?  (I know i could do this easily in jQuery, but unfortunately we're not using jQuery.) Currently I have a script.sh file with the following content:  #!/bin/bash wget -q http://exemple.com/page1.php; wget -q http://exemple.com/page2.php; wget -q http://exemple.com/page3.php;   I want to execute the commands one by one, when the previous finishes. Am I doing it in the right way? I've never worked with Linux before and tried to search for it but found no solutions.