I don't even get what is happening with the lines how to i get rid of them?
I was following  on creating a watch and noticed that when I rendered the watch, some pieces were messed up.  I'm new to 3D modeling and I've just learned Blender, I can't explain it well, so here's a picture:    Other examples:     I don't know if it's a problem with my World texture, the object, or the object's texture/material, so I can't even guess how to fix it. What causes this? Is it possible to fix it?
Hubble's law says that the universe is expanding. How come the Milky Way and the Andromeda galaxies are on a collision course? How will they end up colliding with each other? Intuitive explanation for density of transformed variable? Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf   $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) &amp; y \ge 0 \\ 0 &amp; y \lt 0\end{cases}$$   I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who doesn't know calculus. In particular, I'm trying to explain why the factor $\frac{1}{\sqrt{y}}$ appears out front. I'll take a stab at it:  Suppose $X$ has a Gaussian distribution. Almost all the weight of its pdf is between the values, say, $-3$ and $3.$ But that maps to 0 to 9 for $Y$. So, the heavy weight in the pdf for $X$ has been extended across a wider range of values in the transformation to $Y$. Thus, for $f_Y(y)$ to be a true pdf the extra heavy weight must be downweighted by the multiplicative factor $\frac{1}{\sqrt{y}}$  How does that sound?  If anyone can provide a better explanation of their own or link to one in a document or textbook I'd greatly appreciate it. I find this variable transformation example in several intro mathematical probability/stats books. But I never find an intuitive explanation with it :( How can I change the language for dictation on the fly? With English not being my first language, I usually need support for at least two languages when using features like auto-correct and dictation.  Is it possible to toggle the language which is used for dictation via a shortcut?  As of now, I always have to manually navigate through the menus in the System Preferences which if far from convenient. I've tried to see if there are any pre-defined actions in Automator, but found none. Simple bijection $\mathbb N_0 \times \mathbb N_0 \to \mathbb N_0$ I'm looking for a 'simple' bijection $$ \pi \colon \mathbb N_0 \times \mathbb N_0 \to \mathbb N_0, $$  where 'simple' in this context means that it should be as easy as possible to define and it should be self-evident that said function is in fact a bijection. It's a quest for convenience - not minimal complexity in any rigorous sense.  Here are a couple of examples I came up with - none of which satisfy both requirements:   Let $\pi(m,n) = c(2^m3^{n+1})$, where $c \colon \{2^m3^{n+1} \mid m,n \in \mathbb N_0 \}\to \mathbb N_0$ is the order isomorphism (or in fact Mostowski collapse) of its domain under the natural ordering, Let $\pi(m,n) = \langle n,m \rangle$ - Gödel's pairing function, Let $\pi(m,n) = m \oplus n$ - the number resulting from '' $m,n$ (where we imagine both $m$ and $n$ as in infinite decks of cards whose $i$th element is labeled with its respective $i$th digit). ... I have Ubuntu 16.04 with GNOME shell. I set ctrl+shift for the "Modifiers-only switch to next source" option.   This shortcut conflicts with apps hot-keys. I can't use ctrl+shift+i to open devtools in Chrome, it just switches the layout. In VS code IDE if I press shortcuts with ctrl+shift (for example ctrl+shift+f), shortcuts work but always switch a keyboard layout. When I used Windows this problem didn't exist.  Can I set the ctrl+shift shortcut in such a way that it causes a switch action only after the keys are released and only if this 2 keys were pressed (without additional keys)? Hi I have a question regarding finding the values of limit for the following question.  Let $a, b \in \mathbb R$. Find the limit $$\lim_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$$ Should I put a comma before the last item in a list? Should I put a comma before the last item in a list?     I would like crackers, cheese and some soda.   I would like crackers, cheese, and some soda. Buying shares when the price goes down 2% and selling shares when it goes up 2% Fermi's golden rule and infinite probablity? I am slightly confused about the application of . Which during standard derivations indicates a probability of transitioning from the state $|i \rangle$ to the state $|f\rangle$ of: $$P=\frac{2\pi t}{\hbar^2} | \langle f | \hat V | i \rangle|^2 \delta(E_f-E_i-\hbar \omega)$$ This holds for large values of $t$ but for arbitrarily large values of $t$: $$P&gt;1$$ Which (to me anyway) makes no physical sense since there can't be a probability greater then 1 of been in the final state. If my interpretation is right then how is this problem resolved/allowable? and if it is wrong what part of what I have said is wrong? Prove a assertion concerning Lebesgue space Let $f_n \in L^1$ such that $f_n\rightrightarrows f$. Then I want to conclude that If $\mu(X)&lt;\infty,$ then $f\in L^1$ and $\int f_n\to\int f$, so I want to make use of the Dominated convergence theorem, the thing is that I don't know which would be my dominating function.  I was trying to figure out if the measure could play that role, but after thinking a little bit I have realize that the measure doesn't have to be bigger than the absolute value of the functions of the sequence.  Another thing I was thinking of, is to apply Fatou's lemma, but I can't ensure that my functions are positive.  So, Can someone help me to prove this theorem please ?  Thanks a lot in advance :).    NOTE: I think this theorem is taken from Folland's Real analysis, modern techniques, and their aplications 2nd Edition :), This is to have all the definitions so we can talk the same language as in the book (this is, same notation and theorems or machinery) Custom text color in C# console application? Can you identifiy this short about teenagers on a raft getting swallowed up by an oil slick? The proof I have starts of with $\;xy=0\;$ in a field.   Then $x^{-1}$ exists because it is a field.  Then $x^{-1} xy=x^{-1} 0$.  Therefore $y=0$.  But surely if an integral domain can not have any zero divisors, how can we end the proof by saying $y=0$? Surely then y is a zero divisor and hence the field is not an integral domain? Best way to build a Plugin system with Java How would you implement a Plugin-system for your Java application?  Is it possible to have an easy to use (for the developer) system which achieves the following:   Users put their plugins into a subdirectory of the app The Plugin can provide a configuration screen If you use a framework, is the license compatible with commercial developement? Occasionally, I've come across a webpage that tries to pop open a new window (for user input, or something important), but the popup blocker prevents this from happening.  What methods can the calling window use to make sure the new window launched properly? "Congratulation" vs. "congratulations" I have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty.  $$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm \Delta v_{2} $$ $$ v_{3} \pm \Delta v_{3} $$ $$ \vdots $$ $$ v_{N} \pm \Delta v_{N} $$  Since they're measurements of the same quantity, all the values of $v$ are roughly equal. I can, of course, calculate the mean:  $$ v = \frac{\sum_{i=1}^N v_{i}}{N}$$  What would the uncertainty in $v$ be? In the limit that all the $\Delta v_i$ are small, then $\Delta v$ should be the standard deviation of the $v_i$. If the $\Delta v_i$ are large, then $\Delta v$ should be something like $\sqrt{\frac{\sum_i \Delta v_i^2}{N}}$, right?  So what is the formula for combining these uncertainties? I don't think it's the one given in  (though I may be wrong) because it doesn't look like it behaves like I'd expect in the above limits (specifically, if the $\Delta v_i$ are zero then that formula gives $\Delta v = 0$, not the standard deviation of the $v_i$). In my opinion the accepted answer should permanently stick as only the original question submitter has the ability to accept. is keyword in Python Let n be an even integer. How many different ways can I choose subsets of the set {1,2...,n}