I have the Looting 3 enchantment on my iron sword and hit a few fireballs back at a ghast. Eventually, a fireball collided with the ghast, killing it, and I picked up the three ghast tears it dropped. Three seemed like an awful lot, as I'm used to one, or occasionally two, but three is new for me.  Seeing as I had Looting 3 on my sword, did that effect how many ghast tears I got from killing the ghast, even though the ghasts' own fireball killed it?
I got 2 ghast tears after I thought I deflected a fireball back at the ghast (with my looting 3 sword).  But I was pretty close, so I might have just hit it. I'm not sure.  If I deflect a fireball with a looting sword and it kills the ghast, do I still get the looting bonus?
Find the number of solutions of $x^2=x\mod m$ for any integer $m$.  I was thinking about bringing the $x$ over to the other side and somehow apply chinese remainder thm. When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? I want to change my thesis topic (to the extent that the ethos is still in tact) but my advisor does not agree. What can I do? I am doing a phd where my aim is to solve a problem A which is very interesting. My supervisor has got a lot of connections in a technology B and he claims to be an expert in B. I came to this group because of these accomplishments. But soon I realized that B is not really a great technology for A.   So in my phd proposal I proposed a method which encompasses B but is more general (say R). Now I realize that I do not want to use B at all because my preliminary results are not encouraging. In fact, I am inclined to use E as a base technique which does not have any impact on R.  But my supervisor, who is interested in only publishing in B  and frowns upon everything else (it was a nightmare to convince him to let me work on R) is dead against it. He says that he is an expert in B and his vision of the group is not inclined with me trying other things.  There are other professors in my university who have worked in E and could collaborate but my supervisor won't collaborate with people from outside his kingdom. I also know professors from outside my university who could help me if needed. I could knock the doors of school committee in order to  help me but that would create a lot of problems as my supervisor wields a lot of power and influence everywhere.    Another query is, is it ethical to collaborate with people outside the university (of course after letting my supervisor know) for my PhD work. My Masters supervisor would be happy to help me out.  Edit: After looking at comments, I am thinking that after all, it is MY PhD. Yes, I have spent 1.5 years, but 1.5 years is left. Why should I spend any moment of my life on something I find to be not exciting, particularly less exciting because it is forced on me. And in those 1.5 years I learnt to write well and also learnt 'A' which is important. Its not total waste. My supervisor has his agenda, and why should I give up mine to make him happy? His vision is fine, but he does not have the right to force his vision on me. Sounds simple but I seem to fail every time, that is it turns into scrambled eggs instead. How do you make it so that you can flip it over both without it breaking and before it burns? bash profile works for user but not sudo The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence! I have a scenario where I have multiple threads adding to a queue and multiple threads reading from the same queue. If the queue reaches a specific size all threads that are filling the queue will be blocked on add until an item is removed from the queue.  The solution below is what I am using right now and my question is: How can this be improved?  Is there an object that already enables this behavior in the BCL that I should be using?  internal class BlockingCollection&lt;T&gt; : CollectionBase, IEnumerable {     //todo: might be worth changing this into a proper QUEUE      private AutoResetEvent _FullEvent = new AutoResetEvent(false);      internal T this[int i]     {         get { return (T) List[i]; }     }      private int _MaxSize;     internal int MaxSize     {         get { return _MaxSize; }         set         {             _MaxSize = value;             checkSize();         }     }      internal BlockingCollection(int maxSize)     {         MaxSize = maxSize;     }      internal void Add(T item)     {         Trace.WriteLine(string.Format("BlockingCollection add waiting: {0}", Thread.CurrentThread.ManagedThreadId));          _FullEvent.WaitOne();          List.Add(item);          Trace.WriteLine(string.Format("BlockingCollection item added: {0}", Thread.CurrentThread.ManagedThreadId));          checkSize();     }      internal void Remove(T item)     {         lock (List)         {             List.Remove(item);         }          Trace.WriteLine(string.Format("BlockingCollection item removed: {0}", Thread.CurrentThread.ManagedThreadId));     }      protected override void OnRemoveComplete(int index, object value)     {         checkSize();         base.OnRemoveComplete(index, value);     }      internal new IEnumerator GetEnumerator()     {         return List.GetEnumerator();     }      private void checkSize()     {         if (Count &lt; MaxSize)         {             Trace.WriteLine(string.Format("BlockingCollection FullEvent set: {0}", Thread.CurrentThread.ManagedThreadId));             _FullEvent.Set();         }         else         {             Trace.WriteLine(string.Format("BlockingCollection FullEvent reset: {0}", Thread.CurrentThread.ManagedThreadId));             _FullEvent.Reset();         }     } } Cell copy results in jaggy, aliased output How do I hide Thunderbird from the launcher while running? I have a question for you all.  It's possible to "hide" thunderbird from the unity application bar when thunderbird is running?  For my is unhelpfull see thunderbird on the "mail" tray ( near shutdown button) and the unity "running" application.  If i close thunder with the close button, it don't notify me new email. Are there any guidelines for converting cooking recipes from Regular Ovens to Convection? I was looking to buy a Convection Oven and wanted to know if there are any general differences in baking methods between the two. Can anyone explain how one would convert one voltage range to another? I'm going to need to convert a range of -10 to +10 volts into a range of 0 to +5 volts. How would this be accomplished? Thanks!   Let me say  something more. Inside of a torpedo there are gyroscopes. This gyroscope give -10 volts when the torpedo have 180 degrees of deviation to the west and 10 volts when the deviation is to the east. This signal is DC, so i need to change this range a range: 0 to 5 v DC . Thanks I want to perform performance testing on my test server.  How can I capture workload from production and replay on my test server?   Basically I'm looking for detailed steps so that I can replay the workload from production to my test environment. Sum of reciprocals of numbers with certain terms omitted I know that the harmonic series $1 + \frac12 + \frac13 + \frac14 + \cdots$ diverges. I also know that the sum of the inverse of prime numbers $\frac12 + \frac13 + \frac15 + \frac17 + \frac1{11} + \cdots$ diverges too, even if really slowly since it's $O(\log \log n)$.  But I think I read that if we consider the numbers whose decimal representation does not have a certain digit (say, 7) and sum the inverse of these numbers, the sum is finite (usually between 19 and 20, it depends from the missing digit). Does anybody know the result, and some way to prove that the sum is finite? For what $n$ is $U_n$ cyclic? When can we say a multiplicative group of integers modulo $n$, i.e., $U_n$ is  cyclic?   $$U_n=\{a \in\mathbb  Z_n \mid \gcd(a,n)=1 \}$$  I searched the internet but did not get a clear idea. How do I pass variables and data from PHP to JavaScript? Cannot mount NTFS partition in Ubuntu 13.04 After I installed Ubuntu 13.04, I can't mount my NTFS partition.  Error mounting /dev/sda5 at /media/mrxfly/xFLyDiskData: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda5" "/media/mrxfly/xFLyDiskData"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda5': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option. Understanding English (Listening skills) proof relating to limit definition of e I'm studying the book A Primer for the Mathematics of FinancialEngineering, along with it's solution guide. I've ran into trouble with the solution to question 7 in chapter 1.    The problem is:  Show that $(1+\frac{1}{x})^x &lt; e &lt; (1+\frac{1}{x})^{x+1}$ .   Specifically, I'm having trouble with one step in the solution.    It says that  $$x\ln\left(1+\frac{1}{x}\right)&lt;1&lt;(x+1)\ln\left(1+\frac{1}{x}\right)$$  can be written as   $$\frac{1}{x+1} &lt;\ln\left(1+\frac{1}{x}\right)&lt;\frac{1}{x}, \forall \ge 1.$$  How can the first equality (or is it inequality?) be written as the second? Let $X$ be adapted integrand, for which we know that $E[\int_0^T X_s^2 \, ds]&lt; \infty $. Let $0≤s&lt;t≤T$ and we have some $W∈F_s$ ($F_s$ is $\sigma$-algebra) and we know $E[\int_s^t W^2X_u^2 \, du]&lt;\infty$. I have to show  that $\int_s^t W X_u \, dB_u=W \int_s^t X_u dBu$.  I know that for simple integrands this follows from definition. We also know that for $X$ there exists sequence of elementary integrands $X^n$ such that $E[ \int_0^t (X^n_u-X_u)^2 \, du]$ converges to $0$, when $n \to \infty$. From this one can see that it also holds $E[ (\int_0^t (X^n_u-X_u) \, dB_u)^2]$. I wonder if I can show that it  holds $E[ |(\int_s^t W (X^n_u-X_u) \, dB_u)|] \to 0$ as $n \to \infty$ . (I think I should use Cauchy- Schwarz inequality: $E(XY)^2 \leq E(X^2)E(Y^2)$, but not sure where. If I could show this convergence in $L^1$, it would be enough for my proof. If I rewrite it as $E[E[|(\int_s^t W(X^n_u-X_u) \, dB_u)|  \mid F_s]]$ I don't know if I can put $W$ out of integral. Would it be correct? Any help would be really very appreciated. Thanks. Search for singleton tags on questions