My model is shaded smooth, and autosmoothed. But some edges/faces look sharp. How come? And how do I fix it?
I've been modeling a hermit crab and I don't know why but some areas of the mesh are really dark on some spots, like the legs and the claws.   I hope you can help me fix it.
How do I fix "Error C1033: cannot open program database"? Suppose that:  $0 \rightarrow M_{1} \rightarrow M \rightarrow M_{2} \rightarrow 0$  Is an exact sequence of $R$-modules (for $R$ commutative integral domain). Show that $\mathrm{rk}(M) = \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$    I have shown the inequality $\mathrm{rk}(M) \geq \mathrm{rk}(M_{1})+\mathrm{rk}(M_{2})$, however for the opposite direction I'm lost. I tried to take $N$ as a linear independent subset and tried to decompose it into $N_{1}$ (the elements in $\mathrm{Ker}(g)$) and $N_{2}$ (the elements not in $\mathrm{Ker}(g)$), but I haven't got far, since $N_{1}$ gives us a linearly independent set in $M_{1}$, however $N_{2}$ can give us a linearly dependent set in $M_{2}$.   We define $\mathrm{rk}(M)$ in this case as the supremum over all cardinalities of the linearly independent subsets of $M$ (where the only finite linear combination equaling $0$ implies trivial coefficients for $r \in R$).  Would this be the proper way to show the result? I think I'm missing something important. I have an external sound card which mostly works fine, except that when its first plugged in, or when I turn on my laptop, the volume gets set to 100%. That is, the overall system volume, as shown in the sound indicator.  What I'm looking for is a terminal command that will set that volume to 50%, so that I can run it on login and not have to worry that the first audio I play is going to blare out at me if I forget to turn the volume down. What commands allow you to change that volume, i.e. the one in the sound indicator?  I've poked around in gsettings and dbus, but have been unable to find anything that would let me set the system volume like that. I do know about alsamixer, but that's not the solution I'm looking for, since that doesn't allow me to change the volume using the sound indicator or my laptop's multimedia keys. Are the datum and the ellipsoid the same? What is a Datum?     The Earth is shaped like a flattened sphere. This shape is called an   ellipsoid. A datum is a model of the earth that is used in mapping.   The datum consists of a series of numbers that define the shape and   size of the ellipsoid and it's orientation in space. A datum is chosen   to give the best possible fit to the true shape of the Earth.  in this   article.... My book (Concepts of Physics by H.C. Verma) writes:  It has been reported () that the force between two masses may be better represented by $$F = \frac{G_{\infty} m_{1} m_{2}}{r^2} \left[1 + \left(1 + \frac{r}{\lambda} \right) \alpha e^{-\frac{r}{\lambda}}\right]$$ where $\alpha \approx - 0.007$ and $\lambda \approx 200~\mathrm{m}$.  What is this? Such a horrendous formula! So, what about Newton's? And what's the difference between $G$ &amp; $G_{\infty}$? How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related: I want to get a 360 and don't know wether to get the bigger (250GB), newer, more expensive Elite, or get one of the older, smaller (120GB), last gen ones. I know the arcade is going to be too small to save anything useful  How much hard disk space is recommend? What else is stored besides games? Let's say I have the domain johnsmith.com and I want people to reach me via email, what is the best email username to use?  Some examples:   john@johnsmith.com - redundant john.smith@johnsmith.com - redundant and looks kinda stupid mail@johnsmith.com - makes sense, but looks very "technical" me@johnsmith.com root@johnsmith.com - for the geeks among us ;-)   Of course, technically I can simply say that I will be able to receive *@johnsmith.com, however, for a better user experience I still just want one email address for public presence (website, business cards, etc.).  Any suggestions? "Mornings came and cast a blinding sunlight over everything, and he felt like nothing worthwhile could be accomplished."  For some reason, I feel like "a blinding light" is ok, but if its sunlight, then I should drop the "a" and write "cast blinding sunlight", but I'm not sure why I feel this way.   Can anyone offer some enlightenment?  edit - alternate phrasing, closer to being a literal translation: "Mornings came without warning, flooding the day with a strong sun, and he felt like nothing worthwhile could be accomplished."   I would still like an answer to the technical question of whether I should drop the "a", but would also appreciate knowing if anyone thinks option #2 is a better choice. Sufficient condition(s) for $f'$ to be Riemann integrable Is this correct for Rudin exercise 3.7? Prove the series is convergent This is Baby Rudin exercise 7 of Chapter 3. Prove that the convergence of $\sum{a_n}$ implies the convergence of $\sum{\sqrt {a_k} \over k}$ if $a_n \ge 0$.  Proof:  I will attempt to show that the cauchy criterion is met so $${\sum_{k=n}^m {\sqrt {a_k} \over k}} \le \epsilon $$ for all $n,m \le N_1$. Im disregarding the absolute value since its all positive terms.   Since $\sum{a_n}$ converges, we know that the $\lim \limits_{n \to \infty} a_n =0$ So there exists some $N_2$ such that for all $n \ge N_2$, $$   a_n \lt \ {{(m-n)}^2k^2(\epsilon)^2} $$ I am again disregarding the absolute values because its always positive Let N=max{$N_1,N_2$} then for all $n,m \ge N$ $$\sum_{k=n}^m {\sqrt {a_k} \over k} \le \sum_{k=n}^m {\sqrt {{(m-n)}^2k^2(\epsilon)^2} \over k} \le \sum_{k=n}^m{(m-n)(\epsilon)} = \epsilon $$  Maybe this is just crazy, should I just use Cauchy-Schwarz inequality and forget about this or could I possibly make this method work? How does a wheelie work? So I've been trying to create a mathematical model for an electric motorcycle and began to wonder about the maximum possible torque that could be supplied to the rear driven wheel without having the bike begin to lift up on one wheel.  I found ways to calculate this value online; however, the basic concept as to how the bike actually lifts escapes me.    My problem started when I began to think about what axis the bike will rotate about when it is doing the wheelie.  My first intuition was that the frame and front wheel, together, rotate about the rear axle.  But when I drew a free body diagram of the frame/front wheel system just at liftoff (see below) I made note that the only forces acting about the rear axle, point O, is the force of weight.  This means that an increase in applied torque and subsequently, the applied force Fa, should not effect the rotation about the rear axle.  I know that the applied force on the back wheel is indeed correlated with the propensity for a bike to wheelie, so I considered that the axis of rotation I was choosing was wrong.  If we take the free body diagram above and sum the moments about the center of mass, we would find that an increased applied force would in fact cause the solid body to rotate.  The problem with this understanding is that during rotation, the center of mass of the drawn system should actually rises relative to the surface the bike is moving across.  If the bike were to be truly rotating about its center of mass, then the back wheel would begin to dip below the surface of the road like you might see in a glitchy video game.    So I suspect that the bike is in fact rotating about the back axle, but I don't understand why, please help!  edit: I added the external torque from the back wheel to the frame, which would allow the bike to rotate about the back axle  edit 2:  I suppose that the torque acting on the frame via the engine should not effect the rotation as the movement of a motorcycle can be perfectly replicated by applying a force at the back axle.  A third possible axis of rotation might be the lowest point of the back wheel. How to switch from Resident visa to Tourist visa status in the Schengen area? 1) Alex's house      2) Alex' house     When the noun ends with the letter 's' or 'x', do I need to put 's' after an apostrophe or not?  I remember I read some rules related to this in my school grammar book, but now I've forgotten it. How can I show that "A center of a free group that is non-cyclic is trivial" ? Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $ Let $K\subseteq \mathbb{R}^n$ be a compact set and $E\subseteq \mathbb{R}^n$ a closed set, such that: $$\inf\{d(x,y):x\in K, y\in E\}=0$$ where $d(x,y)=\sqrt{\sum_j(x_j-y_j)^2}$ Prove: $E\cap K\neq \emptyset $  I tried to work with the definitions of compact and closed sets, and I understand that from what's given of the distance between elements in $K$ and $E$, that they are very close,  but couldn't really get further. Any help appreciated. How do I find out which DOM element has the focus? How does the tmp folder work? It stores lots of junk files and takes space My tmp folder is set to /sites/default/files/tmp/ and I checked what's inside and for example there is folder inside called /update-cache-b2903cc4/ it keeps all modules in .zip that I installed via 'Install from a URL'. So why are those modules .zip files are kept there in tmp folder, isn't it a waste of storage? I don't really like it when the site is full of unnecessary files.  Am I supposed to delete these by myself all the time? Position of \caption gets counter incremented twice How to vote on friends / colleagues ' questions (or answers)