I'm modelling a bottle shape. And when I add the subdivision modifier the top and rear of the bottle has its surface seem pinched non smooth (although I have added shade smooth). So I delete the top face, select the vertices and do a grid fill which can be seen in the image attached. But when I increase the viewport quality in my subdivision modifier the top of the bottle seems more square than circle.  What's the best modelling tip so the top of the surface doesnt make that pinched surface?  Thank you.
My problem is simple. I think that the strange deformations on the top are there because there are so many vertices in one face. How do I fix this while maintaining nice topology?  Although I triangulated the top polygon, the problem still persists.
The general consensus on a similar question,  is that "highly significant" is a valid, though non-specific, way to describe the strength of an association that has a p-value far below your pre-set significance threshold. However, what about describing p-values that are slightly above your threshold? I have seen some papers use terms like "somewhat significant", "nearly significant", "approaching significance", and so on. I find these terms to be a little wishy-washy, in some cases a borderline disingenuous way to pull a meaningful result out of a study with negative results. Are these terms acceptable to describe results that "just miss" your p-value cutoff? Let $a&gt;b&gt;0$ and let $n \in N$ satisfy $n \geq 2$.  Prove that $$a^{1/n}-b^{1/n}&lt;(a-b)^{1/n}.$$  If we let $a=x$ and $b=x-1$, then we need to show that $f(x):=x^{1/n}-(x-1)^{1/n}$ is decreasing for $1\leq x$ (which means that $f'(x)\leq 0$ and $f$ is differentiable), and evaluate $f$ at $1$ and $a/b$. Is it possible to use the enumerate/itemize environment within the proof/remark environment in a nice way? How can I fix/repair a corrupted PDF file? I have been playing with Ubuntu for a few weeks now, and I'd like to revert my computer back to it's original - factory - defaults.   On the computer I have a recovery partition (it's a netbook). I went through the process of recovery and everything seemed fine. However, when I restart the computer I'm presented with   grub rescue &gt;   Now, my understanding is that when I installed Ubuntu "side by side" it replaced the MBR or something like it, with GRUB.   I've read on a slew of forums, that I need to use a Windows Recovery Disk.   Here are my issues:   a) I don't have a recovery disk, I have a recovery partition - it's a netbook. b) I don't have an external cd drive.   What I do have is a USB key that has about 1gb of space on it.   Thanks in advance. [[ 0*10%300 ]] works on AIX 6.1 but not on AIX 7.1 (ksh) Ubuntu non LTS to LTS in the future What is the best way to share/distribute Excel macro? I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out.  I have a least squares regression model, with one independent variable and one dependent variable. The relationship is not significant. Now I add a second independent variable. Now the relationship between the first independent variable and the dependent variable becomes significant.  How does this work? This is probably demonstrating some issue with my understanding, but to me, but I do not see how adding this second independent variable can make the first significant. Why is my variable unaltered after I modify it inside of a function? - Asynchronous code reference Is "life" a countable noun in English? I am a learner of English. 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If not, can I specify the output directory of those files ? Maybe I could just write them in /tmp. Pass in an array of Deferreds to $.when() Windows 7 SP1 Windows Update stuck checking for updates I installed Windows 7 fresh and installed SP1. Now, when I try to check manually for Windows Updates it just hangs on the Checking for updates screen.    I tried running the tools in , but this did not fix the issue either:  No matter what I do it just hangs on the "Checking for updates..." screen and goes no further. Does every set have a group structure? I know that there is no vector space having precisely $6$ elements. Does every set have a group structure? Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question Show that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$.      Let $\phi$ be the homomorphism from $\Bbb R[x]$ onto $\Bbb C$ given by   $f(x) \rightarrow f(i)$ (that is, evaluate a polynomial in $\Bbb R[x]$   at $i$).  Then $x^2 + 1 \in \operatorname{Ker} \phi$ and is clearly a   polynomial of minimum degree in $\operatorname{Ker} \phi$.  Thus,   $\operatorname{Ker} \phi = \langle x^2 + 1 \rangle$ and $\Bbb R[x] /\langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$.   My question is:  How is $x^2 + 1$ a polynomial of minimum degree in $\operatorname{Ker} \phi$? From Stewart 7e pg 614 # 9  "One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard th eremor and the fraction who have not hear the rumor. a) Write a differential equation that is satisfied by y. b) Solve the differential equation c) A small town has 1000 inhabitants. At 8 am 80 people have heard a rumor. By noon half the town has heard it. At what will 90 percent of the population have heard the rumor? "  The wording of this is very ambiguous to me and I can't really make sense of it.  They mention a product, so I know that something is being multiplied and that y is a fraction which belongs to the population who have seen it so I think that "have not" heard is a constant, and that y is a fraction taht represents who have. I tried to set this up and it is the wrong answer. I am not sure what they want from that, the English usage is too ambiguous to make sense of it. The complete lack of punctuation is what really does it. Continuous weighted random distribution, biased toward one end I am currently contributing to a particle system for our game and developing some emitter shapes.  My uniform random distribution along a line or along a rectangular area works fine - no problem.  But now I would like to have something like a 1 dimensional gradient in this distribution. This would mean for example lower values are more common than higher values.  I don't know what would be appropriate mathematical terms for this problem, so my search skills are rather useless with this one. I need something that is computationally simple, as the particle system needs to be efficient. What is the rigor behind U subsitution?