Use db_select with multiple conditions of which one needs to apply
How do I add a condition to a query?
Characterising reals with terminating decimal expansions Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$.   This is an unsolved question in my lecture notes. I can only seem to prove the converse direction for this. Would appreciate a solution for the other direction.     For converse direction:   Let the number, in lowest terms, be given by $\frac{l}{m}$ where $m = 2^ \alpha 5^\beta$, for some positive integers, $\alpha$ and $\beta$.    If $\alpha &gt; \beta$, let $k = 5^{(\alpha-\beta)}$. If $\alpha &lt; \beta$, let $k = 2^{(\beta-\alpha)}$.   Then $\frac{l}{m} = \frac{kl}{k2^\alpha5^\beta}=\frac{kl}{10^q}$ where $q = \max(\alpha,\beta)$.   Hence $\frac{l}{m}$ is a terminating decimal. Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian? Let $G=G_1\times G_2$ be a direct product, and let $H\triangleleft G$ be a normal subgroup such that $H\cap G_1=H\cap G_2=\{1\}.$ Then $H$ is abelian.     I considered the commutators of two elements in $H$, trying to show that it must be $1,$ but I don't see how this works. Any hint is very welcomed and appreciated. Thanks in advance. Convert a matrix to a 1 dimensional array How can I prove that the additive group of rationals is not isomorphic to a direct product of two nontrivial groups? I am working through Paolo Aluffi's new GSM text on my own (self-study). On page 63, he asks the reader to     Prove that $\Bbb{Q}$ is not the direct product of two nontrivial groups.   For some context, this is an exercise following a section entitled "The category Grp".  I am assuming that he means "is not isomorphic to the direct product of two nontrivial groups", and I can see two possible ways to proceed with this proof, but have been unsuccessful with either approach.    Approach 1:  Show that the additive group of rationals has a property that is preserved by isomorphism that the direct product of two nontrivial groups does not have or vice-versa.  This seems challenging unless I can significantly narrow down the properties that a direct product of two nontrivial groups that was isomorphic to $\Bbb{Q}$ would necessarily have.  Approach 2:  Considering the section in which this question occurs, show that if $G$ and $H$ are nontrivial groups and $\Bbb{Q} \cong G \times H$, then there are homomorphisms $\varphi_{G}:\Bbb{Q} \rightarrow G$ and $\varphi_{H}:\Bbb{Q} \rightarrow H$ which do not factor or do not factor uniquely through the product $G \times H$.  This would be a contradiction, as $G \times H$ is a final object in the category Grp.  I would greatly appreciate suggestions on how to proceed further with either of these approaches or with alternate approaches. I'm wondering about the period character . used as a shortcut for the local computer name.  You can use it when logging into Windows 7, for example, to specify that the user account you're entering belongs to the local computer rather than to a domain:  .\MyLocalUserAccount   And you can use it within a Windows Management Instrumentation (WMI) query to indicate that the target is the local computer rather than a remote computer.  You can also use it when working with named pipes to for similar purposes.  However, you cannot use it as the UNC network name for the computer, like this:  \\.\MyShare   Does this character have an official name (e.g. "LocalHostToken") and when and where can it be used for this purpose? Command and Conquer 3 exeption in exception handler I have command and conquer 3 from Origin, but when I try to start it, I get the 'exception in exception handler' error and the game exits.   I've tried the Origin launcher fix as well as -runver to make the game run a different version (although this just says that it can't find any version). I run Windows 10 (I know, experimental) but this game worked at one point, and then stopped working suddenly - there wasn't even an update in between.   I suspect that it's got to do with Origin, but any help would be appreciated. Draft mode for pgfplots disconnected phone while installing ROM I recently tried to install a custom ROM in my samsung j6+ but halfway through it my PC turned off. Then the problem starts i decided to reboot my phone but it shows this error &quot;No command&quot; &quot; #Reboot recovery cause is [[check_bootmode]RebootRecoveryWithKey]# Block-based OTA Supported API: 3 # MANUAL MODE v1.0.0# E:Failed to mount / cache: Invalid argument  The error message keeps appearing for just a fraction of a second then disappear and appear again I tried to go to recovery mode but no luck i cant get to it I drained the battery to turn off the device then go download mode but after get to it, it also keep restarting help me please. thank you Baking cloth simulation use only 20% of cpu ressources, how to get 100%? Baking a cloth use only 20% of CPU, inactive process of cpu is 78%, is there a way to use those extra 78% ? Blender 2.75 Windows 10 Search using symbols is broken Are upvotes on competing posts counted per question or per answer for Sportsmanship? The definition of the :     Up voted 100 competing answers   doesn't specify whether each upvote on competing answers to the same question counts towards this criteria, or if it's limited to one "point" per question no matter how many additional competing answers you upvote. Can someone explain how it works? 'was' versus 'had been' When I asked the driver/ to come with me to the temple/ he had been reluctant./ No error.   I think instead of 'had been', there should be 'was'. Even the answer key points that the error is in the 'he had been reluctant' part. But I am not sure why exactly is 'had been' wrong.  If we replace the first part with 'when I had asked the driver', would that make 'had been' in the third part correct? What conservation law corresponds to Lorentz boosts? Noether's Theorem is used to relate the invariance of the action under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of four-momentum.  In the case of angular momentum, the tensor (in special relativity) has 3 independent components for the classical angular momentum, but 3 more independent components that, as far as I know, represent Lorentz boosts. So, what conservation law corresponds to invariance under Lorentz boosts? sudo apt update &amp;&amp; sudp apt upgrade -y now shows the error message E:The package linux-modules-5.4.0-56-generic needs to be reinstalled. But I can't find an archive for it.  and nothing proceeds. How can I fix this problem? Thanks. Difference between "irascible", "fractious", "irritable" and "atrabilious"? It seems that they can all mean "easily provoked to anger"  irascible：Easily provoked to outbursts of anger; irritable.  fractious：Irritable; argumentative; quarrelsome.  irritable：1.Capable of being irritated. 2.Easily exasperated or excited.  atrabilious：1.Characterized by melancholy. 2.ill-natured; malevolent. Can anyone explain how Windows effectively limits the CPU?  Last time I tried some tricks to let my laptop not overheat, so I tried limiting the CPU to 70%.   As for my suprise it stopped my laptop from overheating - even when launching CPU intensive applications which caused my laptop to overheat and shut down, didn't overheat my laptop anymore!  I looked at task manager but the "CPU intensive" application still uses ~95% of CPU and the windows task manager shows a total of 100% CPU usage.  I have limited the CPU usage here ("plugged in" option was on 70% [both min and max] when testing the CPU intensive application):    How does Windows do this magic?   I see 100% CPU usage yet my CPU does not overheat. And I do not see any performance differences.  Does Windows limit the CPU speed? Like, if I have a 2.4 GHz processor, on 70% it will only have 1.68 GHz when limited? How is this possible (changing the CPU speed)? I thought you can only underclock when in BIOS?  If not, how does Windows accomplish this if not by changing the speed?    Side question: If it's about the speed, is there a way to set the CPU max state to 200% ? Why weren't everyone on Haruun Kal made a Jedi? Drush CC all returning "No Drupal site found, only 'drush' cache was cleared" I've tried other solutions, but none of them are specific to my setup. I just started using the new Linux subsystem featured in the recent Windows 10 update. I'm using WAMP x64 v3.0.6, and have successfully cloned my website and got it up and running. At the root of the Linux subsystem, I installed Drush globally with Composer, using the directions given on the .  Typing drush status returns the following when I run it in my default directory:  Drupal version         :  7.50  Site URI               :  http://default  Database driver        :  mysql  Database hostname      :  localhost  Database port          :  Database username      :  root  Database name          :  aerosphere  PHP executable         :  /usr/bin/php  PHP configuration      :  /etc/php5/cli/php.ini  PHP OS                 :  Linux  Drush script           :  /home/bob/.composer/vendor/drush/drush/drush.php  Drush version          :  7.1.0  Drush temp directory   :  /tmp  Drush configuration    :  Drush alias files      :  Drupal root            :  /mnt/c/wamp64/www/drupal-7.50  Site path              :  sites/default   But, as mentioned in the title, drush cc all returns No Drupal site found, only 'drush' cache was cleared.[warning] I assume it has something to do with adding a path to the .bashrc, but I don't know what to add. Any tips would be greatly appreciated!  My question is different from "", they're on a Mac and using MAMP, and I'm using WAMP on Windows. I've tried the solutions offered on that post, but the issue has not been resolved.  I'm obviously having issues connecting to MySQL as I get this when I run mysql command:     The program 'mysql' can be found in the following packages: * mysql-client-core-5.5 * mariadb-client-core-5.5 * mysql-client-core-5.6 * percona-xtradb-cluster-client-5.5      Try: sudo apt-get install .   So I've added these lines to my .bashrc file:  PATH="$HOME/.composer/vendor/bin:$PATH" export PATH="/mnt/c/wamp64/mysql/mysql5.7.14/bin:$PATH"   The top line was added to get drush working. I've checked multiple times, and I have the path correctly set, but it's still not working. Hartshorne Theorem 8.17 A result of Stieltjes Integral While studying the Riemann - Stieltjes integral, I read this exercise in my book:  "Let $f:[a, b]\to \mathbb{R}$ be a bounded function. Denoted $L(P, f)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon&gt;0$, there exists $\delta&gt;0$ such that for every partition $P$ with $|P|&lt;\delta$, we have: $\underline{\int_{a}^{b}}f(x)dx-L(P, f)&lt;\epsilon$."  My question is: Can we generalize this problem for Stieltjes integral, with $\underline{\int_{a}^{b}}f(x)d\alpha$ instead of $\underline{\int_{a}^{b}}f(x)dx$?  Particularly, can we have this theorem?  Let $f:[a, b]\to \mathbb{R}$ be a bounded function and $\alpha$ is a monotonic function on $[a, b]$ . Denoted $L(P, f, \alpha)$ the lower Darboux sum and $|P|$ the mesh of the partition $P$. Prove that for every $\epsilon&gt;0$, there exists $\delta&gt;0$ such that $\underline{\int_{a}^{b}}f(x)d\alpha-L(P, f, \alpha)&lt;\epsilon$ for every partition $P$ with $|P|&lt;\delta$?  I don't know how the mesh of the partition relate to the function $\alpha$.