How to scale the bosses level to mine
What factors determine enemy levels or: How do enemy levels scale to the player character's?
$SU(3)$ irreducible representations with tensor method I am dealing with the tensor product representation of $SU(3)$ and I have some problems in understanding some decomposition.  1) Let's find the irreducible representation of $3\otimes\bar{3}$  we have that this representation trasforms like   $${T^\prime}^i_j=U^i_k {U^{\dagger}}^l_j T^k_l $$  hence I observe that  $$Tr(T)=\delta^j_iT^i_j$$ is an invariant and so  $$T^i_j=\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)+\frac{1}{3}\delta^j_iT^i_j$$  allows me to write $$3\otimes\bar{3}=8\oplus1$$ Here comes my questions: I have heard that this $8$ representation is an "$8_{MA}$" where MA is for "mixed-antisymmetric". The meaning of "mixed-antisymmetric" shold be: "the tensor $\left(T^i_j-\frac{1}{3}\delta^j_iT^i_j\right)$ should be antisymmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes". What does this mean? I see only 2 index in that tensor.  2) Consider this representation: $$3\otimes3\otimes3=3\otimes(6\oplus\bar{3})=3\otimes6_S\oplus3\otimes\bar{3}=3\otimes 6_S\oplus8_{MA}\oplus1$$  and now on my notes I have $$3\otimes6_S=10_S\oplus8_{MS}$$  Where "MS" is for "mixed symmetric": symmetric for an exchange of 2 particular indexes but not for a general exchange of 3 indexes.  I could not demonstrate this last decomposition using tensor method. I started noticeing that: $$3\otimes6_S=q^iS^{k,l}$$ where $S^{k,l}$ is a symmetric tensor But then I am not able to proceed in demonstrating the above decomposition (note: I would like to demonstrate this decomposition using only tensor properties, not Young tableaux). I tried to look on Georgi, Hamermesh, Zee and somewhere online but I have not found any good reference which explains well this representatin decomposition...  EDIT: the demonstration should not include the use of Young diagrams...my professor started the demonstration by writing $\epsilon_{\rho,i,k}q^i S^{k,l}=T'^l_\rho=8_{MS}$ and then stopped the demonstration. How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments? Change multiple filenames by replacing a character The final state of 1000 light bulbs switched on/off by 1000 people passing by What was Natsume hiding in her closet in episode 11? In episode 11 of Tokyo Ravens, what was Natsume hiding in her closet? How to run some code only when the rails console starts, kind of like an rc file? I'd like to assign a frequently used string to a shortcut key, so when I press it, it types it in whatever application I'm in. So for example, when I type Shift-F12, it types "This is wonderful!" in whatever Gnome app I'm in at that time. Story where vampires are created by drop absorbed on neck? I have been trying to identify a book that I read maybe 25-30 years ago (1987-1992), in which there are vampire or vampire-like creatures, but instead of being created in the traditional way (e.g. bite on the neck), something drops a drop of a fluid on the back of their neck, which is then absorbed into the body and transforms them. I have a vague notion that some sort of tree is what creates these drops. The drops may have had a shiny metallic appearance.  I've tried to find this book before and always came up short. I'm starting to think the whole thing was a dream and I never read it at all. But I really feel like it was a book or at least a short story. Exercise $1.8$ of chapter one in Hartshorne. In exercise 1.8 of chap I in Hartshorne algebraic geometry,       Let $Y$ be an affine variety of dimension $r$ in $\mathbf A^n$. Let $H$ be a hypersurface in $\mathbf A^n$, and assume that $Y \nsubseteq H$. Then every irreducible component of $Y \cap H$ has dimension $r-1$.     I refered to a . In this solution, why $f$ is not a unit in $B$? How to assign permanent drive letters to removable USB hard drives I have scripts that expect specific drive letters for hard drives. Windows sometimes assigns the different drive letters (e.g. I expected my Maxtor drive to be E:, but it's now F:, therefore my scripts will fail), depending on the order of how the drives are plugged into my laptop.  In Windows 7, how do I assign a permanent drive letter to a drive? Add space between headings and body in the home of the iPad app It's a pain in the ass for me to quit the app, draw a red circle in another app and return to the app, so...    If you notice the three questions in the bottom, you will notice that the emboldened headings (New Answer, Comment) are stick to the next character. Imperfect.    App Version: 1.4.0.249 Device: iPad 2 (GSM) OS Version: Version 9.1 (Build 13B143) why arcane legacy steps to boot from USB with GPT and UEFI? To run the live AVG rescue "disk" on USB for Windows 10, how is it made to work with a GPT and UEFI system?  (Possible solution listed below.)  I enabled the boot menu so that pressing F12 will display a list to select from.  Also, I put everything USB at the top of the boot sequence and Windows and the HDD at the bottom.  However, I hadn't realized GPT and UEFI are so different from a BIOS.  Because the USB flash drive isn't compatible with GPT it's not being picked up?  This  was suggested:   Open the notebook and press quickly F2 to enter the BIOS. Under the MAIN menu, enable the F12 Boot Menu option. Under the BOOT menu, select Legacy boot and press F10 Save &amp; Exit. While the notebook is rebooting, press F2 again to enter the BIOS. Under the BOOT menu, select as your first boot option the USB HDD stick (your USB stick). Press F10 Save &amp; Exit.    Perhaps this will work, but what is the problem that prevents UEFI boot from registering the thumb drive?  Because it's using GPT and not an MBR?  I don't want to switch to legacy, but stay with UEFI.  The laptop: Excel-Count number of visible cells containing certain string I have a sheet in which I first apply a filter to a certain column to show "Unique records only". Now I have a column which contains, for e.g., values like:  Applepie Applesauce Crabapple Banana Mango   What I need is the count of all visible cells containing the word "Apple". Note that this should exclude the hidden (filtered out) cells. Now I have found out a formula:  `=SUMPRODUCT(SUBTOTAL(3,OFFSET(Sheet1!A:A,ROW(Sheet1!A:A)-MIN(ROW(Sheet1!A:A)),,1))*(Sheet1!A:A="&lt;Text to search&gt;"))`   However the problem with this one is this formula searches for the entire text. NOT just a part of it. How do I modify this formula to return count of cells containing "Apple" i.e. for this example it should return 3 as the result. How do I go about porting Ubuntu Touch to different devices? I would like to port Ubuntu Touch to a device that is currently not supported. What are the requirements for doing this and where do I begin? Derivation of Newton-Euler equations I am in search of a simplified version of the derivation of  (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the center of mass of the body is not at the center of gravity.  I can find elementary derivations for the same system when the center of mass is at the center of gravity, but not for my system in question.    I am using the derivation as background research for a rotordynamics project that I'm working on.  Any help and or references would be greatly appreciated!  :) I'm using the beamer miniframes theme (with subsection=false) and the compress option. Currently the navigation shows the dots for each subsection side-by-side. I would prefer if there would be a horizontal space (e.g. with the width of a dot) between the dots of each subsection. Is this possible? Right now it looks like:  Section 1 oooooo  And I would prefer it to look like:  Section 1 ooo ooo  MWE: \documentclass[compress]{beamer}   \useoutertheme[subsection=false]{miniframes}   \begin{document}   \section{Sec 1}   \subsection{}   \begin{frame}[t]     hi   \end{frame} \subsection{}   \begin{frame}[t]     hi   \end{frame} \end{document}` How can I deploy a connected app from my sandbox environment to my production environment? I built a changeset and I was able to include all my classes, but it was a surprise that salesforce has not provided any option to deploy a connected app.  So how do I go about deploying a connected app? Do I need to create it in every other environment? What is the logic behind the timer of the Sojourner Badge? Layover at Tokyo Narita airport: can I travel outside, and what kind of visa would I need? How to determine the class of a generic type?