Finding ring isomorphism
Ring isomorphism (polynomials in one variable)
How to launch the default (native) application for a given file from Java? Can I tap a creature with summoning sickness to pay "tap an untapped creature you control" costs? I have a  on the battlefield and I played a vampire earlier this turn. Can I tap both to transform Chosen of Markov even though I just played the vampire?  Extra Example: I play  to put two 1/1 white bird tokens into play. Can I now tap a both of them and another creature I control to pay Battle Screech's flashback cost of tapping three white creatures?   Obviously these creatures couldn't use any tap abilities until my next turn, but since the tapping is coming from a different source, I figured the situation might be different. Partial Sums of Geometric Series Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on Why does the mirror modifier sometimes give me an overlapping mesh? When I add a mirror modifier it sometimes doesn't mirror correctly, giving me an overlapping mesh. How can I fix this? Reprojecting raster from lat/lon to UTM in R? How does background blur (bokeh) relate to sensor size? This is a somewhat theoretical question.  Suppose I first take a photo of a subject using a full frame sensor DSLR, with a given lens (say 50mm prime lens at f/3.5).  Now suppose I exchange the camera for an APS-C sensor DSLR (with a 1.6× crop factor). I keep the same lens (same focal length, same aperture) and I step back a few meters in order to maintain the field of view (at least keep the same magnification of the subject). I now take a second photo.  Clearly depth of field will have increased between the two photos. But what about background blur (for example, trees at infinity)? Will I have the same amount of background blur, or will that have changed?  I have read somewhere that background blur depends on the physical aperture size. In this case the physical aperture (physical focal length divided by f/stop) stays the same. But should this number be taken in relation to the sensor size? In which case with the smaller APS-C sensor, the physical aperture will be relatively bigger, which would mean more background blur. This would be rather counter-intuitive as we usually consider it to be more difficult to get background blur on an APS-C camera.  Please give the reasoning behind the answer. I would answer the question myself using this  but I can't manage to get it to run on my computer. Let $a&gt;0$, show that for $x&gt;0$, $1&lt;f(x)&lt;2$, where $$f(x)=\frac{1}{\sqrt{1+x}}+\frac{1}{\sqrt{1+a}}+\sqrt{\frac{ax}{ax+8}}$$  I could take the derivative, find the maximum of the function and conclude. But that involves heady algebra and you have to solve a high degree polynomial. Is there an easier way simply using inequalities? Thanks, much appreciated How to disable the keyring for SSH and GPG? How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$? I have tried a little bit to solve the problem which goes as follows:   My intuition says that there exist no $f:\Bbb R\to\Bbb R$ such that $$f(g(x))=x^{2018}\text{ and }g(f(x))=x^{2019}.$$  Note that $$f(g(f(x)))=f(x)^{2018}\implies f(x^{2019})=f(x)^{2018}$$  Similarly, $$g(x^{2018})=g(x)^{2019}$$ Putting $x=1$ in $f(x^{2019})=f(x)^{2018}$, we get $f(1)=f(1)^{2018}$ and thus $f(1)=0$ or $f(1)=1$.  Similarly, putting $x=1$ in $g(x^{2018})=g(x)^{2019}$ we get $g(1)=g(1)^{2019}$ and thus $g(1)=0,1,-1$.  Now, I can't proceed further. Can anybody solve it? Thanks for assistance in advance. Why doesn't 'find' show this file? Rebel flight suits include an ejection harness, Biggs tells Porkins to eject. This seems to suggest that Rebel fighters have an ejection system.  How would they operate for different fighters? Does the whole cockpit separate? Do they function like current aircraft ejection systems - if so what protects the pilot from the vacuum of space? consider the following subsets of complex plane $$\Omega_1=\left\{c\in\Bbb C:\begin{bmatrix}1&amp;c\\\bar c&amp;1\\ \end{bmatrix}\text{ is non-negative definite } \right\} $$  $$\Omega_2= \left\{c\in\Bbb C:         \begin{bmatrix}         1 &amp; c &amp; c \\         \bar c &amp; 1 &amp; c \\         \bar c &amp; \bar c &amp; 1 \\         \end{bmatrix} \text{ is non-negative definite } \right\}$$  Let $$\bar D=\{z\in\Bbb C:|z|\le1\}$$ Then 1) $\Omega_1=\bar D,\Omega_2=\bar D$  2). $\Omega_1\neq\bar D, \Omega_2=\bar D$  3). $\Omega_1=\bar D, \Omega_2\neq\bar D$  4). $\Omega_1\neq\bar D, \Omega_2\neq\bar D$  How to proceed? Thank you. How to accumulate values of each two rows across a line in linux? I might end up teaching philosophy in Finnish lukio/gymnasium. I will not get an opportunity to practice teaching it - I do get to practice teaching mathematics a fair deal, though. (The situation is somewhat unfortunate.) I have taken subject studies in philosophy at university. They amount to around 60 credits (ECTS).  Suppose I give the students an exam, which asks them to write an essay or two. After that my task is to grade the exams in a fair way and comment them in such a way that the students can learn from the feedback.  -  Suppose the task was to write an essay on the problem of universals - nominalism and realism, say. Let us say 6 points is the perfect score for this task.  I would expect the students to define nominalism and realism (2 points, maybe?) and explain the problem (2 points). Remaining two points for taking some stance and arguing for it - realism is more reasonable because so and so. Partial credits for demonstrating only partial understanding.  -  Am I missing some important aspects of philosophical thinking? Should I emphasize the different parts of an answer in a different way? I suspect my perspective is influenced by fairly extensive mathematics education - is there something particular I should watch out for? I am trying to assign an image texture to an Image Texture node in 2.80. Very simple script - I'm just starting to learn how this stuff works.  This is what I have. It creates an image and and IT node, but it doesn't assign the one to other. Can anybody help? I've searched around, but can't find it in another question.  import bpy  #create blank image bpy.ops.image.new(name="TestImg", width=1024, height=1024)  #add image texture to object, to hold baked lighting mat = bpy.context.view_layer.objects.active.active_material image_node = mat.node_tree.nodes.new('ShaderNodeTexImage')  #assign image to image texture node image_node.image = "TestImg"   Thanks in advance. How do you use the Dungeon Defender's Portal Gun? The topic pretty much sums up my question. I have not yet figured out how the gun operates aside from the fact that it creates Portal portals. The weapon description indicates that it deals 250+ base damage, but how is that damage applied to the monsters? Under the U.S.'s Copyright Law, is it an act of copyright infringement if we changed the color of another artist's image to black and white? Table column not align if give color for Table entries My code follows:  \documentclass{book} \usepackage{color,colortbl} \begin{document}  \begin{tabular}{ll&gt;{\color{red}}p{20pc}} a &amp;1 &amp;Test \end{tabular}  \end{document}   The output was:    Some unnecessary vertical space came before the last column. If I remove the tag \color{red} then everything works fine, how can I fix this?  Above said issue was fixed based on the suggestion given by David Carlisle and CarLaTeX, but the same problem was there if I use the supertabular environment, I used supertabular package for auto breaking table and the code follows:  \documentclass{book} \usepackage{color,colortbl,supertabular} \begin{document}  \begin{supertabular}{ll&gt;{\leavevmode\color{red}}p{4pc}&gt;{\leavevmode\color{black}}l&gt;{\leavevmode\color{black}}l&gt;{\leavevmode\color{red}}p{4pc}} a &amp;1 &amp;Test &amp;a &amp;1 &amp;Test\\ a &amp;1 &amp;Test &amp;a &amp;1 &amp;Test\\ \end{supertabular}  \end{document} Which statistics to use?