Do you need to claim the one ring for your own to be detected by Sauron?
Why didn't Sauron find Bilbo when he put on the ring like Frodo?
Evaluation of $\displaystyle \int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$   $\bf{My\; Try::}$ Let $\displaystyle I = \int_{0}^{1}\frac{x\ln x}{\sqrt{1-x^2}}dx\;,$ Put $x=\cos \phi\;,$ Then $dx = -\sin \phi d\phi$  and Changing Limit, We get  $$\displaystyle I = -\int_{\frac{\pi}{2}}^{0}\cos \phi \cdot \ln(\cos \phi )d\phi = \int_{0}^{\frac{\pi}{2}} \ln(\cos \phi)\cdot \cos \phi d\phi$$  Now Using Integration by parts, We get  $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{\sin^2 \phi}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{(1-\cos^2 \phi)}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\sec \phi d\phi-\int_{0}^{\frac{\pi}{2}}\cos \phi d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-\left[\sin \phi\right]_{0}^{\frac{\pi}{2}}$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-1$$  Now How can I solve after that, Help Required, Thanks At 9th level, the Armorer Artificer (from Tasha's Cauldron of Everything) gains the &quot;Armor Modifications&quot; feature :  You learn how to use your artificer infusions to specially modify your Arcane Armor. That armor now counts as separate items for the purposes of your Infuse Items feature: armor (the chest piece), boots, helmet, and the armor’s special weapon. Each of those items can bear one of your infusions, and the infusions transfer over if you change your armor’s model with the Armor Model feature. In addition, the maximum number of items you can infuse at once increases by 2, but those extra items must be part of your Arcane Armor.  This special weapon is called 'Thunder Gauntlets' (a simple melee weapon) for the 'Guardian' Armor Model, and 'Lightning Launcher' (a simple ranged weapon) for the 'Infiltrator' Model. But I am wondering which Artificer Infusions are appropriate for this special weapon ? Is it only the 'Enhanced Weapon' and 'Radiant Weapon' infusions, or are there others ? Map from real numbers to real numbers as abelian groups How to transit through Delhi without a visa? I have read a lot on this subject on the Lonely Planet forum and it looks like the staff on ground can transfer your bags through the Delhi airport if you have a connecting flight without you having to go out to check them in again and therefore needing a visa. I refer of course to the situation when you go with 2 different airlines, because otherwise the luggage is transfered automatically.  I posted a  and mentioned it briefly there, however I think this subject deserves a separate question and a detailed answer.  Does it depend on the type on an airline? I have read that Jet is no problem, what about AirIndia and IndiGo? And what about the incoming flight to Delhi from Europe or USA, do they all can hand over you luggage to the Indian airlines and pick it up again on the way home? Do you have to contact them before and explain your situation? Or check in your luggage directly to your desired destination? The kernel and range of the powers of a self-adjoint operator Suppose $L: V \rightarrow V$ self-adjoint (on a finite-dimensional space $V$); $b$ is a real number. Show   The minimal polynomial has distinct roots; $\ker(L) = \ker(L^k)$ for $k\geq1$; $\operatorname{im}(L) = \operatorname{im}(L^k)$ for $k\ge 1$; $\ker(L-bI) = \ker((L-bI)^k)$ for $k\geq1$;     My thoughts:  1) I think I'm supposed to assume root is repeated and reach a contradiction but I'm not sure how to proceed mathematically with that.  2-4) pretty sure there's some huge theorem that I'm missing. How do I extract all the external links of a web page and save them to a file? How do I extract all the external links of a web page and save them to a file?  If you have any command line tools that would be great. Looking for Anime with a prince faking being mentally handicapped hiding a giant mech suit wreaking havoc This is all I can remember.  There are four worlds whose people and technology were all swapped so humans ended up with high tech mech suits that they used to kill each other. There was a supposedly handicapped prince who faked being mentally handicapped and had a giant mech suit hidden underground that he eventually used to wreak havoc on earth.  The protagonist also had a suit and he saved the day. He was in love with a girl who was from another world and when he saved the day, all the people and technology from the different worlds were sent back to their original one causing the girl to leave him. She had colored hair and the final scene was her waking up somewhere with some children commenting on her hair.  There may or may not have been a reference to the protagonists scars in the shape of the constellation of orion on his body.  Any ideas? I've searched the internet for two years trying to find it. Finding the internal name and display name for a list column I am using SharePoint Server 2007 Enterprise with Windows Server 2008 Enterprise, and I am using publishing portal template. I heard for SharePoint list/list column, it has an internal name which could be used for programming (as identifier for list/list column), and also has a display name (which is showed for end user for list name or list column name).  How to find and set such internal name and display name for list/list column? Why are passports checked at the check-in counter, Immigration and even at the gate? I was wondering, why there are passport checks at the check-in counter, Immigration and even at the gate?    For example, I was at Istanbul flying to either UK or US. There's a security check at the check-in counter asking a bunch of questions about my immigration status - even more than the Immigration officer at the border. Also, at the gate, there's also Security officer checking my immigration status and passport asking the same questions.    I thought that would be the responsibility of an Immigration officer rather than some third party company?   The thing I'm curious the most is they don't even know which countries this passport can go to with or without visa. They have to go back to the counter and check with the system which takes a long time. I was wondering why they hire these kind of companies to slow down the process? What is time dilation really? Please will someone explain what time dilation really is and how it occurs? There are lots of questions and answers going into how to calculate time dilation, but none that give an intuitive feel for how it happens. Are the contents of a loot box determined at the time it is awarded or when it is opened?  For example, if you collect multiple loot boxes before a special event but opened them during the special event, would they have the potential of spawning rewards from that event? Lily Potter chose to die instead of sacrificing her son Harry to Voldemort. In doing so, protective enchantments were created that protected Harry and made him less vulnerable to Voldemort and Voldemort's attempts to kill Harry.   Yet, I don't understand how Lily's enchantments, when Voldemort stole Harry's blood in the graveyard scene in Goblet of Fire (chapter 33, The Death Eaters), were helpful to Voldemort at all.     ‘He took my blood,’ said Harry.   ‘Precisely!’ said Dumbledore. ‘He took your blood and rebuilt his living body with it! Your blood in his veins, Harry, Lily’s protection inside both of you! He tethered you to life while he lives!’   Deathly Hallows - page 568 - Bloomsbury - chapter 35, Kings Cross   Yet I wonder about the following canon information:    Lily's enchantment was contingent upon Petunia Dursley giving Harry a home, which Petunia     grudgingly did&#185;. It was the blood bond between Harry and Petunia, plus the fact that Petunia gave Harry a home, where he could return to once per year, that sealed Lily's   protective enchantments and made them strong. Voldemort was never granted a home at the Dursleys, and in fact never stepped foot into the Dursleys' home at any point in canon. Never having been given a home at the Dursleys, how, then, did Lily, Petunia, and Harry's blood bond exist within Voldemort? Or did it? If it did, would it be because ? Lily's enchantments broke the moment Harry turned 17 and could not protect Harry any more&#178;. According to the 's page on Voldemort, Voldemort was 69 years old when he stole Harry's blood. If Lily's enchantment broke for Harry at age 17, why would the enchantments work for Voldemort when he was 69? Dumbledore tells Harry in Order of the Phoenix that Voldemort would not possess Harry because the love that fills Harry -- Lily's love -- is a force that Voldemort detests so greatly that he cannot bear to come into contact with it&#179;. Yet the love Lily infused into Harry runs in his veins; Voldemort took Harry's blood, the blood that is imbued with Lily's love. How can he bear to be in contact with the love given to Harry in his own veins?   Given this canon information, why did Lily's enchantments work for Voldemort?  &#185;Half-Blood Prince - chapter 3, Will and Won't and Order of the Phoenix - chapter 37, The Lost Prophecy &#178;Half-Blood Prince - chapter 3, Will and Won't &#179;Order of the Phoenix - chapter 37, The Lost Prophecy Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$ Suppose $(M,d)$ a metric space. I want to show that      If every continuous real-valued function on $M$ attains a maximum, then $(M, d)$ is compact.   I was trying to do this by assuming $M$ non-compact and showing explicitly a function which does not attain a maximum. If $M$ is not bounded it's enough to take the distance from a fixed point as we can always find a sequence which "exits" every compact and pushes the distance at infinity. But what if $M$ is bounded? Benefits & Practicality of Virtual Machines I have been living under a rock for the past 5 - 8 years, and am just now getting up to speed with virtualization, virtual machines and platforms like VMware or VirtualBox.  I think I am starting to get them, but there are two concepts about VMs that I'm just choking on for some reason; one has to do with their intrinsic benefit to the enterprise, and the other has to do with their practicality when being used.  So I understand that you can have multiple VMs running on the same physical machine, all doing their own "thing" as if they were separate machines. So let's say I want to make a nice little virtual network of servers in my home office so I can have a big sandbox to play inside of for all my projects. I set up 2 physical machines as servers, and on each of them I have, say, 4 virtual machines running (1 might be an app server, another might be a RDBMS, another might be a message broker, etc.).   Besides saving me money (as I only have to provide 2 physical machines instead of buying 8 servers), what instrinsic benefit/purpose do these VMs serve here? I don't care how clever virtual machines are, if my computer only has 8GB of RAM, and I have 4 VMs running on it, those VMs only get 8GB of RAM to share between them. Putting 4 VMs on my server doesn't endow it with 4 times that amount of RAM! So, as far as I see it, VMs save you money on hardware, but just end up bogging down that hardware as you have multiple machines competing over the same pool of resources. What am I missing here? Can VMs communicate with each other over your network using high-level protocols like TCP/IP, HTTP, FTP, etc.? Otherwise, it just doesn't make sense to implement all these VMs if you have to feed them separate and independent chunks of data/requests to process. Practical hyperparameter optimization: Random vs. grid search Asume the following search queries: osx, cocoa, iphone, xcode, applescript, mac, carbon    Searching for osx, cocoa, iphone or xcode like:   http://stackoverflow.com/search?q=osx   Results into searching by tag:   http://stackoverflow.com/questions/tagged/osx   While searching for applescript, mac and carbon like:   http://stackoverflow.com/search?q=applescript   Results into searching by string.  Yes, I know how to search by tags using brackets: [applescript] But why are the queries above interpreted differently? All queries are valid Stack Overflow tags! Why not convert all queries into search by string or search by tag? What is the logic behind? Tag popularity? It seems rather inconsistent to me. Studying for CISSP these choices seemed limited:     What is the advantage of digital signatures over message authentication codes?         Digital Signature provides integrity verification while message authentication code does not   Digital Signature provides confidentiality while message authentication code does not   Digital Signatures provide authenticity while message authentication code does not   Digital Signatures works faster than message authentication codes      Using the following chart as a reference, I'm leaning towards #2, but none of the choices really fit properly…  Cryptographic primitive | Hash |    MAC    | Digital Security Goal           |      |           | signature ------------------------+------+-----------+------------- Integrity               |  Yes |    Yes    |   Yes Authentication          |  No  |    Yes    |   Yes Non-repudiation         |  No  |    No     |   Yes ------------------------+------+-----------+------------- Kind of keys            | none | symmetric | asymmetric                         |      |    keys   |    keys   Hopefully an expert here can clarify. I know this may be a tough or confusing question, but I have numerous existing materials I created and reuse for a project, which were all prepared for Blender Internal.  Now, I want to start the transition to Cycles, but I've hit a roadblock. How can I transition my materials without completely starting over? Or should I just forget it and start with fresh materials? What's the best way to build a string of delimited items in Java? Why does arXiv have a multi-day lag between submission and publication? If you go on the  (now, 8th December 2020, 19:24 Italian time), there is for example the article &quot;Exploring the Usage of Online Food Delivery Data for Intra-Urban Job and Housing Mobility Detection and Characterization&quot;. This article is under the heading &quot;8 December&quot;. But if you , it was &quot;Submitted on 4 Dec 2020&quot;. Why there is a lag between submission time and the header under which it appears for recent publications? I guess the arXiv staff have to approve the article before is being published .... is my guessing correct?