Let $A$ be a primitive matrix (a square nonnegative matrix some power of which is positive). Is $AA^T$ necessarily primitive?
Is it true that if $A$ is a nonnegative primitive matrix, then $AA^T$ is also primitive? Obviously $A^T$ is primitive but in general product of primitive matrices is not primitive.  Any hint?
Sam Weller in The Pickwick Papers: What accent is Dickens portraying? In Dickens' Pickwick Papers, there's a character "Sam Weller". Weller's dialogue is written somewhat phonetically, I presume, but I'm struggling to understand what accent Dickens is trying to portray. The main peculiarities of Weller's speech are using "v" where there should be a "w" and a "w" when there should be a "v". For example, he says "wery" instead of "very" and "avay" instead of "away". Weller is supposed to be from London, but this doesn't seem like any kind of London accent I've heard. Is this a particular archaic accent?  More importantly, what is Dickens telling us about Sam Weller by having him speak like this? I just visited  and noticed that my profile picture is not the same as on all other sites.  According to  the image will be synchronized when synchronizing the complete profile. I did that but the image is still the same.  Then I wanted to change the image in the Area51 profile directly - but I can only change to a gravatar image and can't use the new and fancy Stack Exchange image.  Is that a bug? Finding net magnetic and electric force on charged particle This is from my textbook, it is not an assigned problem, but I want to understand.   It says:      Consider the situation in the figure, in which there is a uniform electric field in the x direction and a uniform magnetic field in the y direction. For each example of a proton at rest or moving in the x, y, or z direction, what is the direction of the net electric and magnetic force on the proton at this instant?   I believe I need to use the equation   $$ F_{net}=(q\overrightarrow{E})+q(\overrightarrow{v} \times \overrightarrow{B}) $$  But I'm not sure exactly how. We've just started to learn about this, and I want to get a head start. Could anyone put me on the right track? Explaining Horizontal Shifting and Scaling Space of bounded continuous functions is complete Prove $4(x + y + z)^3 > 27(x^2y + y^2z + z^2x)$ Prove that, for all positive real numbers $x$, $y$ and $z$, $$4(x + y + z)^3 &gt; 27(x^2y + y^2z + z^2x)$$  I've tried expressing it as a sum of squares, but haven't got anywhere.   Hints are also welcome. What is the difference between "likelihood" and "probability"? map collections I am new to Apex and just starting to understand using maps to avoid loops within loops and hitting limits. My trigger below updates opp line items with the internal cost from another object using a map and the one value - "Service_Name".  My issue is I need to update another field on the Opp line item with "Agent Fee" in the same way  - but there are 4 criteria to get the right Agent Fee from another object. I cant see how do so this other than have a loop of agent Fees object with the opp line loop? How else can I do this? Is it possible with Maps ?  trigger sectortest on Opportunity (after update) {          for (Opportunity eachopportunity : Trigger.new){                                        //Get costs for the Opps FY and put in map         List&lt;Internal_Costs__c&gt; costs = [SELECT Id, Financial_Year__c, Service_Name__c, Standard_Cost__c  FROM Internal_Costs__c WHERE Financial_Year__c =: eachopportunity.Financial_Year__c];          Map&lt;string, Decimal&gt; costmap = new Map&lt;string, Decimal&gt;();         for (Internal_Costs__c eachcost : costs){                                         costmap.put(eachcost.Service_Name__c, eachcost.Standard_Cost__c);                         }                 //Get Line Items for Opp         List&lt;OpportunityLineItem&gt; opplines = new List&lt;OpportunityLineItem&gt;();           opplines = [SELECT Id, DS_Status__c, Country__c, Product2Id, UnitPrice FROM OpportunityLineItem WHERE OpportunityId =: EachOpportunity.Id];           List&lt;OpportunityLineItem&gt; opplinesupdate = new List&lt;OpportunityLineItem&gt;();                //assign cost to line items              for (OpportunityLineItem EachOppline : opplines) {                                                                                              decimal cost = costmap.get(EachOppline.Service_Name__c);                                                                 EachOppLine.Internal_Cost__c = cost;                                                                             opplinesupdate.add(EachOppline);                                                                                                                                                        }              update opplinesupdate;                        }                       } Error message "sudo: unable to resolve host (none)" Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$. I am looking to prove that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$. In the Wikipedia article:    They say that this statement has been proven by E. H. Moore in 1893.  How to go about proving the theorem? I know first I need to generate a subset, prove that it's a subfield, and then assume they are two and show it's unique.  But how to generate it in the first place? Consider the set of polynomials of the form $x^{p^m}-x=0$? Is there a way to show that it's a subfield without checking all the axioms? How to check if a point is inside a rectangle? How can I completely disable internal Mic and Webcam I want to disable the internal Microphone on my laptop and the internal Webcam completely that they're no longer selectable, and no longer available?  I will only use my external Webcam, and my external (USB) headset.  The internal audio should still be available for playback. Name of short sci-fi story involving a musician who is punished for listening to Bach If I open up many tabs in Chrome, the Tabs start to shrink. This is usually a normal behavior if the tabs would use the whole availible space, BUT in my case the tabs shrink too much. They don't use up the whole availible space anymore, but only go until somwhere at three quarters of the window. The more tabs I open, the larger the availible space gets until it reaches a maximum. This strikes me as somewhat not so normal.  Another funny thing is, if I use a second Monitor to extend my Desktop, Tabs will be smaller on the second Desktop and will only fill half the availible space from the beginning. For example right now I have 6 tabs open, which fill out approximately half the availible space. If I open more tabs, only the tab size reduces. This has not been like that when I first installed the browser.  This is what it looks like:    Is there any solution for this?   I hereby explicitly mean NO extensions. I found enough extensions to handle tabs. I just want them to behave normally without any of those tab-extensions. Re-Installing Chrome does NOT work, I tried that. Is a contradiction enough to prove a set equality to $\varnothing$? how to not commence a command depending on player health? I'm on a MacBook Pro (15-inch, 2018) with Mojave 10.14.1. When I connect MBP to a external displays (either via HDMI or via Thunderbolt 2 adapters), the temperature raises sensibly (i.e., CPU temperature lies constantly over 90°) and fans start running fast (i.e., more than 50%) frequently, even if I am doing very simple tasks (e.g., writing in Word with a couple of Chrome tabs open with stackoverflow).  I'm not sure that the problem started with Mojave or if it isn't actually related to the OS version.  I'm wondering if there is a way to limit this annoying overheating as well as fans activity, while using external monitors. This dreaded issue started at some time after upgrade to OS X (Yosemite) 10.10.3. accountsd uses about 60% CPU constantly, making the laptop hot and noisy.  I'm not using iCloud at all.  Killing it doesn't help, because it starts again quickly.  Probably related question, but it's about iOS: Why are Marketing Cloud timestamps not stored in the same timezone as Sales Cloud? Port Forwarding to a VMware Workstation Virtual Machine