Smallest $n$ such that $U(n)$ contains a subgroup isomorphic to $\mathbb Z_5 \oplus \mathbb Z_5$
Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups
I have a lightning component that displays Knowledge Articles based on Topic IDs that it is configured for. This works great so I went to create my test coverage for it and discovered that the inserted test Knowledge Articles can only ever be 'Draft' making my tests fail since the apex class only looks for 'Online'. Instead of rewriting my component I decided to overload the apex method so that when called without the status parameter it passes in 'Online' allowing my tests to pass in 'Draft' instead. However, the first method signature does not get called from the component resulting in null for the status parameter.  Here is the component controller:  ({     "retrieveArticles" : function(component, event, helper) {         var action = component.get("c.returnArticlesWithTwoTopicIds");         action.setParams({             mainTopicId : component.get("v.mainTopicId"),             secondaryTopicId : component.get("v.secondaryTopicId"),             limitAmount : component.get("v.limitAmount")         });          action.setCallback(this, function(response) {             var state = response.getState();             if (component.isValid() &amp;&amp; state === "SUCCESS") {                 // handle SUCCESS             }             else if (component.isValid() &amp;&amp; state === "ERROR") {                 // handle ERROR             }         });         $A.enqueueAction(action);     } })   Here is the apex class:  public with sharing class KnowledgeArticleVersionCtrl {     @AuraEnabled     public static List&lt;KnowledgeArticleVersion&gt; returnArticlesWithTwoTopicIds(String mainTopicId, String secondaryTopicId, Integer limitAmount) {         return returnArticlesWithTwoTopicIds(mainTopicId, secondaryTopicId, limitAmount, 'Online');     }      @AuraEnabled     public static List&lt;KnowledgeArticleVersion&gt; returnArticlesWithTwoTopicIds(String mainTopicId, String secondaryTopicId, Integer limitAmount, String status) {         // build query string         List&lt;KnowledgeArticleVersion&gt; articles = Database.query(query);         return articles;     } }   Is there something about the component that would cause it to not use the first signature, the one it should match, in place of the second one, which it shouldn't match? I have added a custom/secondary query to a template file/custom page template; how can I make WordPress use my custom query for pagination, instead of using the main query loop's pagination?  Addendum  I have modified the main loop query via . Why isn't pagination working, and how do I fix it? Find all $x$ such that $x^6 = (x+1)^6$. Silencing "Your disk is almost full" notification After upgrading to macOS Sierra, I'm getting the notification that "Your disk is almost full. Save space by optimizing storage.":    The options appear to be to store my files in iCloud, automatically delete files, or manually delete files:    My problem/irritation is that I have 80GB free of my 440GB volume.  The question: is there a way to silence this notification in a (semi-)permanent fashion, or to change the threshold it uses for the notification? Put the book back on the table.   I'm having trouble. I think it is a preposition. 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Presumably, the usual definition is $[r\exp(i\theta)]^{1/n} = r^{1/n}\exp(i\theta/n)$ for $\theta \in [0,2\pi)$, but I have yet to see this anywhere. Is this because it has bad properties? For instance, according to this definition is it true that for all complex $z$ it holds that $(z^{1/a})^b = (z^b)^{1/a}$? Please be kind, I am an electronics nub.  This is in reference to getting an LED to emit photons.  From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.  In an example experiment (involving a primary dry cell, a SPDT switch, a resistor and an LED) it states that the resistor MUST be connected to the anode of the LED.  In my mind, if the electrons flow from negative to positive, wouldn't the electron flow run through the LED before the resistor; thereby making the resistor pointless? 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Tables:  Ingredients [     IngredientsID INT [PK],     IngredientsName VARCHAR ]  Recipes [     RecipesID INT [PK],     RecipesName VARCHAR ]  IngredientsRecipes [     IngredientsRecipesID INT [PK],     IngredientsID INT,     RecipesID INT ]   Query:  SELECT     Recipes.RecipesID,     Recipes.RecipesName,     Ingredients.IngredientsID,     Ingredients.IngredientsName FROM     IngredientsRecipes      INNER JOIN Ingredients     ON IngredientsRecipes.IngredientsID = Ingredients.IngredientsID      INNER JOIN Recipes     ON IngredientsRecipes.RecipesID = Recipes.RecipesID WHERE     Ingredients.IngredientsName IN ('salt', 'water', 'flower')   I am currently constructing my query using ASP.NET C# because of the dynamic nature of the WHERE clause.  I bites that I have to construct the query in my code-layer instead of using a stored procedure/pure SQL, which in theory should be much faster.  Have you guys got any thoughts on how I would move all of the logic from my code-layer to pure SQL, or at least how I can optimize the performance of what I'm doing?  I am thinking along the lines of temporary tables:  Step one: SELECT IngredientsID FROM Ingredients and INSERT INTO temp-table  Step two: SELECT RecipesName FROM Recipes joined with IngredientsRecipes joined with temp-table.IngredientsID What does it mean to "align" partitions? I am familiar with what partitions are, but I saw , and realised I didn't know what "aligned partitions" are.  So what does it mean to "align" partitions? What are the benefits, and the downsides?