(I don't believe this is a duplicate to , because not only am I using a different proof, but also an axiomatisation that could perhaps be seen as controversial) I am a post graduate student of pure mathematics that hasn't published anything yet. Hypothetically, let's say that there's an established result in mathematics that was stated and proven using a popular axiomatisation. Let's say that if you state and prove the same result using a different (non-standard) axiomatisation, then the result becomes (perhaps debatably) more elegant. Is it possible for paper like this to be worthy of publication? If so, are there any specific journals that you think might be more likely to accept such a paper? Slightly more detail: The established result uses ZFC as axiomatisation, my approach uses ZFC + Atoms as axiomatisation. The result that I'm restating and reproving concerns general mathematical structures.
I found a better proof for a theorem than a proof from a published paper. Is it possible for me to publish my proof with the same theorem citing that paper?
In H. P. Lovecraft's The Case of Charles Dexter Ward, Dr. Willett      Enters Joseph Curwen's dungeon and resurrects a dead person identified as No. 118 by reciting the incantation of the Ascending Node over his salts.   Dr. Willett is told by      The resurrected Joseph Curwen, impersonating Charles Dexter Ward, who he secretly murdered,   that   " 'twas Number 118, and I conceive you would have shook had you looked it up in my list in t'other room."  No. 118 himself gives Dr. Willett a note asking the doctor to      kill Joseph Curwen.   It soon becomes clear that No. 118 is opposed to the nefarious dealings that have been transpiring and desirous of being an ally of Dr. Willett.  Who is No. 118?  Earlier in the story,      The grave of Ezra Weeden, a primary instigator in Joseph Curwen's initial downfall and the romantic rival of Curwen, is robbed. There doesn't seem to be any other mention of Weeden in the 20th century occurrences, so without a further connection the passage seems superfluous.   The shared goals of these two people seem to indicate that No. 118 may, in fact, have been that person, but the      Note given by No. 118 to Dr. Willett in eighth century Latin seems to indicate someone much older than Ezra Weeden.   It also occurred to me that No. 118 could be      The recently murdered Charles Dexter Ward himself. Ward's reference to killing Dr. Allen (who is actually an alias of Curwen) and dissolving his body with acid and No. 118's mention of doing the same to Curwen seem to support the idea, but that still doesn't explain the archaic note. Ward is described as writing in a somewhat modern style, at least as opposed to Curwen. It also doesn't explain why Curwen would want to murder Ward if he was going to resurrect him later anyway. Is $\int \frac{1}{2x} \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$ Reasoning for $\frac{\ln|x|}{2}+ C$ :  $$\int  \frac{1}{(2x)}  \, dx = \frac{\ln|2x|}{2}+ C$$   Check: By taking derivative we get $\frac{1}{x}$  Reasoning for $\frac{\ln|x|}{2}+ C$ :  $$\int  \frac{1}{2x}  \, dx = \frac{1}{2}\int  \frac{1}{x}  \, dx =\frac{\ln|x|}{2}+ C$$  Check: By taking derivative we get $\frac{1}{x}$  Question: Is  $\int  \frac{1}{2x}  \, dx $ equal to $\frac{\ln|2x|}{2}+ C$ or $\frac{\ln|x|}{2}+ C$? Find a plane that passes through a point and is perpendicular to 2 planes Find an equation of a plane that passes through $p(1,5,1)$ and is perpendicular to planes $2x+y-2z = 2$ and $x+3z=4$.  I basically need the 2 other points to make the vector and perform the cross product.  Since $ax+by+cz+d=0$ is the form of a plane. Can I obtain the points as $(a,b,c)$ of the 2 planes given? Also, how can I set them up to obtain the points? There are 100 ropes in a bag. In each step, two rope ends are picked at random, tied together and put back into a bag. The process is repeated until there are no free ends. What is the expected number of loops at the end of the process? Is there a way to indicate to  how/where to find (paths to)  tools such as python, nmap, php and so on?  I ask this because when I schedule a job using crontab -e, I always need to specify the full path of python, nmap and whatever other tool I want to use. SQL Server: Examples of PIVOTing String data Not every boolean function is constructed from $\wedge$ (and) and $\vee$ (or) Changing Login Logo After modifying the code in my functions.php file to display a different logo on my login page, I'm getting a blank square instead.  I've added a custom .png image (326x67) to my (child) theme's image folder, and the code I've added to functions.php is as follows:  function custom_loginlogo() {     echo '&lt;style type="text/css"&gt;     h1 a {background-image: url('.get_bloginfo('template_directory').'/images/login_logo.png) !important; }     &lt;/style&gt;'; } add_action('login_head', 'custom_loginlogo');   Could it be a permissions problem (like an .htaccess file blocking the image)? Is there any bidirectional 5v-3.3v level shifter? Is there any IC that interfaces any 3.3V Input/Output to 5V Output/Input? I need it primarily for an Arduino Due but if there any bidirectional IC that works like that it would be great.  Some people advised me to use the SN74AHC125 and CD4050 ICs, but I don't understand how they work or how to interface with them. The graph of the function $f (x)$ is given.  How many different real roots does the $f (4-3x^2)=0$ equation have?  Here is possible solution:  $$\Bigg [{4-3x^2=-2 \\ 4-3x^2=4} \Longrightarrow x=\left\{0,\sqrt 2,- \sqrt 2\right\} $$  Then, here is different solution:  $$f(x)=x^2-2x-8$$ $$f(4-3x^2)=0\Longrightarrow (4-3x^2)^2-2(4-3x^2)-8=0 \Longrightarrow 9x^4-18x^2=0 \Longrightarrow x=\left\{0,\sqrt 2,- \sqrt 2\right\} $$   Problematic point. Here, I assumed the function is quadratic. But, obviously, this function may not be quadratic.  My questions:  Question $-1:$ Is the first solution completely correct?  Question $-2:$ Can we say that, the second solution is completely and definitely wrong? If so, is it possible to add something to this method and turn it into the right solution? Why can't Python's raw string literals end with a single backslash? Which Harry Potter works are considered canon? There are many different Harry Potter works including:   books short stories movies card games video games toys amusement parks web content   Which ones are considered to be canon? RAID10 vs. RAID5 for data files We are trying to evaluate the potential performance improvements that could be gained by switching an existing applications .mdf files to a RAID10 LUN vs. the existing RAID5 LUN they are living on right now. The transaction log already lives on a RAID10 LUN.   So the question is, if we move data files to RAID10 would the end user see performance improvements in the GUI? or would it be just faster writes to the data files when a checkpoint occurs and the changes get written to the data file but no improvement would be seen at the end user level? How can I prevent Overflow for the Gamma function? I have a Dirichlet distribution from which I'm maximizing $\alpha$ by calculating the log likelihood with the following equation  $p\left(s|\alpha\right) = \sum\limits_{i=1}^O\log\left(\frac{n_i!}{\prod\limits_{j=1}^kn_{ij}!}\frac{\Gamma\left(\alpha_0\right)}{\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)} \prod\limits_{j=1}^k \frac{\Gamma\left(n_{ij}+\alpha_j\right)}{\Gamma\left(\alpha_j\right)}\right)$  I have a python script to calculate the log likelihood. It works for small values, but when $n_{ij}$ gets high $\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)$ and $\Gamma\left(n_{ij}+\alpha_j\right)$ python runs into overflow error (the max for math.gamma is between 171 and 172).   Is there a way to change the likelihood function so that $\Gamma\left(\sum\limits_{j=1}^k\left(n_{ij}+a_j\right)\right)$ and $\Gamma\left(n_{ij}+\alpha_j\right)$ don't run into overflow errors. Can I just divide the values in $\Gamma$ by for example 100, if I then compare the likelihood between $p(s|\alpha)$ with different $\alpha$ values do the best $\alpha$ values still have the highest likelihood? Bullied boy given immense powers by an alien race who destroys the human race Does the curvature of spacetime theory assume gravity? Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form &quot;gravity wells.&quot; Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing? SHOWPLAN permission denied when including execution plan in Data Explorer If I select the "Include execution plan" checkbox in the Data Explorer, the query fails:     SHOWPLAN permission denied in database 'StackOverflow'.     I see that  following maintenance. I don't know whether there was any recent maintenance. It's been several days since the data was updated and longer since an update was deployed, if that's related. Names of close-voters are not visible in the post notice but in the revision history and timeline I am not a user with close/reopen votes privileges on Travel Stack Exchange, therefore I can't see the names of the close voters :    However, they are visible when going to the revision history:    or the timeline of the post:    This also happens when I am not logged in: I cannot see the banner (and so if the question has been closed), but from the revision history/timeline of the post I can get that information.  Shouldn't names of close-voters be completely hidden from people without close/reopen privileges (even if the revision history is a little hard to find)? What's the meaning of 90-plus? What's the meaning of 90-plus? More than 90? If so, please tell me more ways to say "more than 90". Thank you! My local hackerspace has a CNC machine.  I can give them my Gerbers and they can print out the PCB.  The machine does not plate VIAs.  I need to do this after the CNC machine is finished.  What is the best process and materials to use?