How to know if my research problem is interesting or not? I have completed my masters in mathematics. I want to pursue PhD in mathematics. I want to frame a research question and write papers in my field.  But some  questions are bothering me:   How does one know that a research problem is interesting and after solving it, one will be able to publish in a good journal? I know the famous journals in my field. But after reading them, how will I decide myself which problem will be beneficial to solve? Also I have seen there are lots of unsolved problems given at the end of a paper in a journal. If I don't understand or find any interesting problem should I try to solve the problems given at the end of a paper? Does it mean the problems stated at the end of a paper are interesting that's why they are stated as problems?
How to choose a good research problem? I am working to get a PhD, maybe next year this time around. Currently, this is my second year. I have published 3 papers. All of them are not about one problem but consider different problems. My strategy to find a research idea/problem is given below.  1 - Read papers whose titles are either interesting or I have some apriori understanding of those titles.  2 - Understand those papers as best as I can. That is, I try to understand each detail presented in the paper except the simulation results (this is because I think simulation results are hard to reproduce).  3 - I analyze the paper and try to find a very small problem which can be addressed (i.e. I can solve it) by the methodology of the paper.  4 - If I am successful at step 3 I start working on that problem otherwise I repeat the process from step 1.  By applying this strategy I have been able to write 3 papers and I have submitted a fourth (I am not satisfied with those papers because at very best they can be considered average papers). But my concern is that the problems addressed in those papers do not belong to one area. As far as I have seen, for the profiles of some of the renowned researchers in my field their PhD work is focused on one area. One main thing I console myself with is that almost all of those researchers had good supervisors. My supervisor does not even read the draft/reviews of my papers and the suggestions that he provides during the meetings are so broad that the problem becomes intractable. Under these circumstances what are your opinions: Is there any better strategy to do research?   I will be very thankful to you for providing me suggestions or commenting on my dilemma.
Messed up Blender models when exporting to Unity3D I have modeled a simple pocket watch in Blender. Every time I import it into Unity3D, regardless of whether I export it from Blender as an FBX or 3ds file, it always comes out missing faces! Why is this happening? I have never had problems importing models into Unity3D like this before.  Blender Screenshot    Unity Screenshots     It seems to me that different faces appear when I rotate it differently. How can I prevent this? Thanks! Removing intercept from GLM for multiple factorial predictors only works for first factor in model Disable flagging on old chat messages In response to the effect  is referring, I am proposing one of two possible scenarios:   Disallow flags on chat messages older than X hours, or Remove old flagged posts from the transcript, but no suspension occurs (as in the aforementioned question). Creating fishnet grid Shapefile in QGIS? How do I create a fishnet shapefile using QGIS?   The equivalent task of "Create Fishnet" in ArcGIS. How to plot the first n rows of a table using pgfplots? When using pgfplots, is there a way to plot only the first n rows of a given table ?  Considering the following MWE file:  \documentclass[tikz]{standalone}  \usepackage{tikz} \usepackage{pgfplots} \pgfplotsset{compat=newest} \usepackage{amsmath}  \begin{document}      \begin{tikzpicture}         \begin{axis}[%             width=16cm,height=8cm,             view={-45}{65},             scale only axis,             xmin=200,xmax=500,             xlabel={data1},             ymin=0,ymax=100,             ylabel={data2},             zmin=0,zmax=1,             zlabel={data3},         ]         \addplot3 [             thick,smooth,             color= darkgray,             solid]             table[row sep=crcr] {                 250 0 0\\                 250 25 0.2\\                 250 50 0.3\\                 250 75 0.2\\                 250 100 0\\             };          \addplot3 [             thick,smooth,             color= darkgray,             solid]             table[row sep=crcr] {                 450 0 0.5\\                 450 25 0.1\\                 450 50 0\\                 450 75 0.1\\                 450 100 0.5\\             };         \end{axis}     \end{tikzpicture}% \end{document}   How can I plot only the first n=4 rows of each table and ask pgfplots to stop reading the table once this row is reached ?  Of course, for the above example, this seems useless, but when huge data tables are used, this could be extremely usefull, in particular to use the same data and focus on different parts of the table in different figures. Prevent Use of the Back Button (in IE) Output of which command used for input to cd I would like to take the output of a which command, and cd to the parent directory. For example, say I have the following:  which someprogram   With output:  /home/me/somedirectory/someprogram   And I would like to cd to the directory that someprogram lives in:  cd /home/me/somedirectory   I'd like to accomplish this in one line. What is the most elegant, tricky, short way to do this? Where can I find every gnome? No matter where I look, I just can't find gnome number [insert number here]. Where can I find every gnome in the game? Set Theory: Tree Property Why does the tree property hold for regular cardinals but not singular cardinals? (I.e. There exists a tree of height $\kappa$ with countable levels and no cofinal branch for $\kappa$ a singular cardinal) Yesterday I read Modern English:A Practical Reference Guide written by Marcella Frank, and she gives a paradigm about tenses on page 50. The page shows tenses in active voice and passive voice; she said these four tenses are exceedingly rare:   shall/will be being offered has/have been being offered had been being offered shall/will have been being offered   Why are these tense so rare? Are they normally replaced by other tenses? An inequality about Stirling numbers For all positive integers $n,r,k$ that $n=rk$, how to prove the inequality $$(r-1)!^k\le \frac{c(n,k)}{S(n,k)}\le (n-k)!$$ $c(n,k)$ is unsigned Stirling numbers of the first kind and $S(n,k)$ is Stirling numbers of the second kind.  Any help would be appreciated! Is there any way to recover deleted files which may have since been overwritten? I deleted lots of files &amp; folders on my laptop and then I put a new files in the same folders. I need to recover the deleted files. I tried a lot of recovery software and I couldn't recover my old files.   I read that if you refill the folders with new files after deleting old ones then I can't recover them again. Is that true?   What should I do? VirtualBox Toolbar is hidden! How to show it? Desktop icons rearrange after using remote desktop connection I sometimes remote into my desktop PC (1900x1280) from my laptop (1280x900).  When I do, Windows (Vista) on the desktop PC rearranges all my desktop icons.  I could understand this if the RDP session's desktop size was too small to fit them in, but it's not.  I have about 12 icons, which do fit on the laptop's resolution (I've tried).  Why would Windows rearrange them all like this each time? Fact  The intersection of a closed set $A$ and a compact set $B$ is closed.  Background  I wanted to prove that the intersection of closed and compact sets is compact. There might be other ways, but I am not interested in them for now and am looking to prove the above statement.  Relevant Facts  I don't have much idea what to use. $A^c$ is open. Every cover $\cup_{i\ge1}U_i$ of $B$ contains a subcover $\cup_{i=1}^kU_i$. I might want to prove $A\cap B^c$ is open. Limit points may be another points to consider but I don't get any idea in that direction.  I also don't have that $B$ is closed otherwise it would be trivial.  Some Clarification  I am aware that compact sets are not closed in arbitrary topological spaces. The reason why I was motivated to believe tha intersection of closed and compact set is compact is true is: See Matt E.'s Answer      So if $K$ is compact in an arbitrary topological space (which is just to say that   it is a compact topological space when given its induced topology) and     $L$ is closed then $K \cap L$ is a closed subset of $K$ in its induced topology   Is it true if $A$ and $B$ are not whole spaces?  I would appreciate any hints. While I've done quite a bit of travel now and back myself to handle situations when it comes to border guards, sorting accommodation and / or transportation, one thing I still struggle to come to terms with is haggling in the markets, be it for food, clothing or other.    Image © Peter Morgan, 2014   What is the best way to go about this? I'm generally either worried I'll offend them, or that they're trying to rip me off anyway, so it's a weird combination of awkwardness inside my head ;) Better than premium Is there something higher (better) than the word premium, or does it mean the best? Also, is there something in between premium and deluxe?  Graphically: Does any word fit here? > Premium > Does any word fit here? > Deluxe I know how to successfully duplicate an object by using  bpy.ops.object.add_named(name = 'TemplateObjectName')   If the template object named 'TemplateObjectName' has animations, particle systems and modifiers attached to it, the previous call will create a duplicate object that also has those components. However, if I duplicate an object using   template_object = bpy.data.objects['TemplateObjectName'] new_object = bpy.data.objects.new('NewObjectName', template_object.data) collection.objects.link(new_object)   how do I attach the template object's animation, modifiers, particle systems...? How to make IntelliJ IDEA recognise code created by macros? I try to solve this problem. I seems to come close to the end but I can't get the conclusion. Can someone help me complete my proof. Thanks          Show that the polynomial $h(x) = (x-1)(x-2)\cdots(x-n) + 1$ is irreducible over $\mathbb Z$ for all $n\ge1$ and $ n\ne4$.      Suppose $h(x) = f(x) g(x)$, then we must have $f(i)g(i) = 1$ for all $i = 1,2,...n$. So both $f(i)$ and $g(i)$ are $1$ or $-1$. In either case, $m(x) = f(x) - g(x)$ has degree smaller than $n$ and have $n$ different roots ($1,2,...,n$). So we must have $m(x) = 0$. Then $h(x) = f(x)^{2}$. So $n$ must be even. Let $n = 2k$. Because $f(x)$ has degree $k$, there are $k$ values from $\{1,2,...,2k\}$ at which $f(x)$ is $1$ and $k$ values at which $f(x)$ is $-1$.  This is where I got stuck. Hope some one can help me solve this. Thanks.