I have a hoodie with two cat-headed holes punched in. If i just fill a face in it, i get it filled up but with no vertices at all inside the shape which will mess up my weight painting. I'd like to fill them in and also have vertices inside.
I have a large hole in a mesh that I'm trying to fill:    I've been trying an approach like this:    I'm finding it quite tough, since the number of vertices around the perimeter of the hole don't match a grid.  Is there a better approach to filling a hole like this?
Induction proof (bitstring length) Theorem : The number of bitstrings with the length $x$ that begin with $1$ and/or end with $0$ is  $3 \times 2^{x-2}$.  I know there are easier ways to prove this but I must figure out how to do it with induction. Why is the last digit of $n^5$ equal to the last digit of $n$? monitor files (à la tail -f) in an entire directory (even new ones) I normally  watch many logs in a directory doing tail -f directory/*. The problem is that a new log is created after that, it will not show in the screen (because * was expanded already).  Is there a way to monitor every file in a directory, even those that are created after the process has started? I am using an APEX batch to process and insert large amounts of data. Essentially I would like it to process every row to catch any errors with the data and then rollback the entire batch if a single error is found. Is there any simple way to do this?  I have tried using a Save Point, but because they are not serialisable, it doesn't work across the entire batch.   Just to clarify, by error I mean an error that I have defined, error with validation, etc. Not an Exception thrown by the system. One Object won't Show up in Final Render even though it shows up in the Preview Render I have a model of a building with a sidewalk around it.  Both show up when I switch to rendering mode in both Blender Render and Cycles Render mode.  But:  when I hit F12 for a final proper render, the building shows up -- but the sidewalk doesn't.    I've checked the normals and I thought the normals seemed pointed in the right direction.  I've set the Clipping on the Camera to a high number.  I removed all the materials from the sidewalk and added a new material-- the problem persists.  I've exported the blend as an FBX file and the Sidewalk shows up fine in Unity.  Just in final renders, it doesn't show up.    Here is a blend file: .  I tried to destroy everything unrelated to the issue and label things in a clear way.    Thanks. Fibonacci Recurrence Relations Solve the recurrence relation $f(n) = f(n − 1) + f(n − 2)$ with initial conditions $f(0)=1$, $f(1)=2.$   So I understand that it grows exponentially so $f(n) = r^n$ for some fixed $r$.  This means substituting this $r^n = r^n-1 + r^n-2$ which gives the characteristic equation of $r ^ 2 - r - 1 = 0$. I'm not 100% sure where to move on from here. Often when I mistype a command such as ls (e.g. I hit ENTER before I type 's') there is a long (~2s) delay after the terminal displays:  bash: l: command not found...   I can understand the reasons for a similar delay after an incorrect password is entered, per . But why delay after an unrecognized command? Does FAIL_DELAY in /etc/login.defs affect this also? Using the properties of real numbers, verify commutativity on complex numbers. I have just started self-studying Linear Algebra after a 3 year hiatus from mathematics (in an extended neuroscience foray), and I want to ensure that I am sufficiently verifying commutativity of complex numbers by using the properties of real numbers.  My attempts...  (1) Commutativity of Addition:   Verify that $w + z = z + w$ for all $w, z \in \mathbb{C}$.  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{16mm} = (a + c) + (bi + di) \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{19mm} = (c + a) + (di + bi) \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{13mm} = c + (a + di) + bi \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = c + (di + a) + bi \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{17mm} = (c + di) + (a + bi) \hspace{11mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{13mm} = z + w \hspace{34mm}\text{by definition of }\mathbb{C}$$  $$\blacksquare$$  This seems a bit verbose to me - is it acceptable to combine steps? For example, rather than:  $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{13mm} = a + (bi + c) + di \hspace{10mm}\text{by associativity in }\mathbb{R}$$ $$\hspace{17mm} = a + (c + bi) + di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ can I instead write: $$w + z = (a + bi) + (c + di) \hspace{10mm}\text{by definition of }\mathbb{C}$$ $$\hspace{48mm} = a + (c + bi) + di \hspace{10mm}\text{by associativity and commutativity in }\mathbb{R}$$?  (2) Commutativity of Multiplication:  Verify that $wz = zw$ for all $w, z \in \mathbb{C}$.  $$\hspace{-14mm}wz = (a + bi)(c + di) \hspace{24mm}\text{by definition of }\mathbb{C}$$ $$\hspace{4mm} = a \cdot c + a \cdot di + bi \cdot c + bi \cdot di \hspace{10mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{9mm} = a \cdot c + bi \cdot c + a \cdot di + bi \cdot di \hspace{10mm}\text{by commutativity in }\mathbb{R}$$ $$\hspace{35mm} = c \cdot a + c \cdot bi + di \cdot a + di \cdot bi \hspace{10mm}\text{by multiplicative commutativity in }\mathbb{R}$$ $$\hspace{1mm} = c(a + bi) + di(a + bi) \hspace{20mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{5mm} = (c + di)(a + bi)\hspace{34mm}\text{by distribution in }\mathbb{R}$$ $$\hspace{4mm} = zw \hspace{55mm}\text{by distribution in }\mathbb{R}$$ $$\blacksquare$$  This also seems a bit wonky to me. Any and all suggestions on clearing up my verification, reasoning, etc. would be greatly appreciated! How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$ Prove that for $x,y,z\in [1,2]$ the following inequality holds: $$\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}.$$ I tried to apply the Cauchy-Schwarz inequality or the power mean inequality, but my attempts were unsuccessfull, so I am asking for help. GTA V for PC exited unexpectedly I recently ordered the GTA V PC from Steam and when I finished installing and launch the game. It gave me "Grand Theft Auto V has exited unexpectedly". I tried "safe mod" and every option available, but none of them work. I checked some forums and found a lot of people having the same problems. What could be the possible cause? I'm using a laptop with these specs:  CPU: i7 4700m GPU: AMD HD8970M RAM: 8GB  I'm pretty sure my laptop is way beyond the minimum specs. Does someone know how can I enter the game? A malevolent computer with AI takes over a woman's house with the intent of hybrid computer/human procreation. The evil computer seals off the house with the woman in it and keeps her prisoner while it prepares. I read the tale sometime in the late 80's or the early 90's. It was one of many of my missing books that got yardsaled by my in-laws when I wasn't looking. It may also have been made into a movie, but I didn't see the film. How widespread is the practice of delegating LoR writing to the applicant? At least two questions (, ) on this site indicate that in more than a few isolated cases at least, letters of recommendation are in fact written by the applicant and only signed off (or perhaps rephrased somewhat) by the recommender, who would actually be responsible for writing the letter.  Is there any evidence about the prevalence of this practice that goes beyond anecdotes? I realize that cross-country (cultural) difference may play a role. How do open files behave on linux systems? Question involving discriminant of quadratic congruence in elementary number theory. Obviously, this suggested edit should never have been approved. Because it's very, very minor.  Is it acceptable for me to "rollback" this edit? Does the suggested editor lose the +2 rep when I roll it back? Should I comment on one of his questions, explaining not to make too minor edits like this?  Is there anything I should do to notify the reviewers that approved  too minor suggested edit? Postfix SMTP banner show multiple hostnames We have a Postfix SMTP server that's bound to two IP addresses and serves mail for two different domains. We can't change the domains to both use the same, single IP. Both IP addresses have reverse DNS   1.1.1.1 reverses to mail.domain1.com 2.2.2.2 reverses to mail.domain2.com   In our Postfix config I have  myhostname = mail.domain1.com myhostname = mail.domain2.com  inet_interfaces = 1.1.1.1, 2.2.2.2  smtpd_banner = $myhostname Mail Server   (And some other stuff, which I think is irrelevant)  Using , running the smtp test command on mail.domain2.com returns everything as OK, however running it on mail.domain1.com returns an error because Postfix is identifying itself as 'mail.domain2.com' in the SMTP banner, how do I get it to return the correct banner based on the external IP address used? Is there a specific reason for having a very short window for passengers to get to the boarding gate before closing it? I am not a frequent traveler but it's been like this with all the flights I have been on. Here is the most recent example:  Below is my boarding pass    As you can see Gate Closes at 20:20  Here is the departures board at 18:32, clearly it says that they will announce the boarding gate at 20:10  ?!    I was hoping they will do that earlier but at 19:41 it's still the same    In fact they announced it at 20:11 but since I was freaking out and had to leg it to the gate I didn't have the time to take a photo.  You might think 9 minutes is enough, well below are the times required to reach the gates from the closest place to them     And that's for a healthy young person, no way my grandmother could be able to be at the gates within 9 minutes.  Is there a specific reason? it's not like they allocate the gate dynamically! The staff must have known about the gate hours ago as I don't expect the pilot to drive the airplane from the garage to the gate within 9 minutes? Beryllium Vacuum Sphere Boat/Aircraft How to insert Bengali text in IEEE conference paper? I am writing a paper for an IEEE conference using IEEEtran.cls. The primary language of the paper is English but my work deals with Bengali language. I want to know how do I insert some Bengali words such as পারে in the paper. Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ I'm undergraduate student of mathematics.  I need to prove: $$\sum_{k=0}^{n} \binom{2n}{2k}= 2^{2n-1}$$ Can you please help me