It's quite usual to read :  "the time needed to factor n by NFS algorithm is exp(...formula with ln(n)...)"  But I can't find to which unit of time this formula refers ? Is it really time ? Or number of operations ?   Thanks
I'd prefer as little formal definition as possible and simple mathematics.
Decidability of a predicate. I have the following problem:  Let the following predicates be: $P1, P2, Q1, Q1 : R \to \{0,1\} $ .  It is given that $P1 \lor P2$ and $Q1 \lor Q2$ are semidecidable and $P2 = \lnot Q2$  What can it be said about $P1 \lor Q1$?  I have searched all over the internet and I simply cannot understand the concept of decidability of a predicate, let alone a logic operation with predicates. Biblatex + Xelatex does not display accents Building a wormhole We regularly get questions about wormholes on this site. See for example  and . Various wormhole solutions are known, of which my favourite is  because it's closest to what every schoolboy (including myself many decades ago) thinks of as the archetypal wormhole.  The trouble is that Visser has pulled the same trick as  of starting with the required (local) geometry and working out what stress-energy tensor is required to create it. So Visser can tell us that if we arrange exotic string along the edges of a cube the spacetime geometry will locally look like a wormhole, but we know nothing about what two regions of spacetime are connected.  My question is this: suppose I construct a Visser wormhole by starting in Minkowksi spacetime with arbitrarily low densities of exotic matter and gradually assembling them into the edges of a cube, how would the spacetime curvature evolve as I did so?  I'm guessing that I would end up with something like Wheeler's bag of gold spacetime. So even though I would locally have something that looked like a wormhole it wouldn't lead anywhere interesting - just to the inside of the bag. I'm also guessing that my question has no answer because it's too hard to do any remotely rigorous calculation. Still, if anyone does know of such calculations or can point me to references I would be most interested. Why is there free space at the end of NTFS Partitioned Drives? I've been wondering this for a while, why is there free space at the end of a drive that was formatted to NTFS in windows?  You can only see the unallocated space in Linux. So why is it there? Does it serve a purpose? ResultSet exception - before start of result set Disable Debug Log Programmatically I'm trying to disable WP_DEBUG_LOG if and only if debug.log exists. I'd like to hook into wp_footer and test if the file exists and if so disable my debug log. All I've found though is that WP_DEBUG_LOG is a constant and can only be changed from the wp-config.php file which is too early for my case. Is there a way to change it from a constant on install and keep it working as normal?   My only other thought is to create an option on install in the options table and just check it every time wp-config loaded to see if the value has changed but I was wanting to avoid that.   Granted I could check if the file exists before I define WP_DEBUG_LOG but somebody would have to view a page twice before debug log actually exists and is detected by the file_exists() (since it's run very early) which is not optimal.  Does anybody know of a workaround to programmatically turn off WP_DEBUG_LOG? I tried installing Office 2007 in Ubuntu with Wine but it was throwing an error after installing and also when I tried to open a PowerPoint document and save it. Has anybody gotten Office 2007 installed without any issues? Please help me. Addition is to Integration as Multiplication is to ______ Addition is to Integration as Multiplication is to ______ ? Everyone knows that definite integration  is "a way to sum continuum-many terms" in a rough sense. Can we "multiply continuum-many factors"  in a similar sense? Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$ How to delete Windows.old in Windows 8 It seems to be a common thing that a Windows Update creates a Windows.old folder under C:\Windows.old My question is now, can it be deleted with Windows 8 and how can I do that?  If I try to manually delete it in Windows Explorer it does not let me, a permissions issue. Calendar.getInstance(TimeZone.getTimeZone("UTC")) is not returning UTC time Placing point over pixel with maximum value falling in grid overlay using QGIS Maximal ideals of polynomial rings in infinitely many variables Let $k$ be an algebraically closed field. Nullstellensatz states that the maximal ideals of the polynomial ring $R=k[X_1,\dots,X_n]$ are precisely those of the form $\langle X_1-a_1,\dots,X_n-a_n\rangle$, with $(a_1,\dots,a_n)\in k^n$.     What if we are working with infinitely many variables, say $\{X_i\}_{i\in I}$, being $I$ an infinite set? Again, the ideals of the form $\bigl\langle\{X_i-a_i: i\in I\}\bigr\rangle$, with $(a_i)_{i\in I}\subseteq k$ are maximal (even if $k$ is not algebraically closed), but what about the converse? Giving edit reputation bonus for same user for same post multiple times On Stack Overflow, I saw some users editing the same question multiple times, and getting the 2 point reputation bonus for each time.  I saw it during review of a suggested edit (some months ago, I forgot the question that's why I'm unable to paste the link here). I rejected it and gave the reason in the "Other" reason field.  Most of the time I saw that users first formats the code, and then after approval they edit the title and fix the grammar.  Why is this allowed?  My point is, if an user gained 2 reputation points for a particular edit, then why give another 2 points again for the same post? Because the second edit on same question/answer means that there were some mistakes or misses in their previous edit. Configure mouse speed (not pointer acceleration!) Is there way to increase the mouse speed in KDE4? I don't want any pointer acceleration, it's just the mouse speed that I want to change.  Edit: Unfortunately, editing the xorg.conf is not an option for me, because I want the users to be able to configure the mouse speed themselves and it is company policy do deny users permission to change the xorg.conf. ‘So the boy ... the boy must die?’ asked Snape, quite calmly.   ‘And Voldemort himself must do it, Severus. That is essential.’   Deathly Hallows - page 551 - UK Hardcover - chapter 33, The Prince's Tale   Dumbledore tells Snape it is 'essential' that Voldemort be the one to kill Harry, I'm assuming in order for the piece of Voldemort's soul in Harry to be properly killed as well.  But why?   Hermione destroyed the Hufflepuff cup; Ron destroyed the Slytherin locket; Neville killed Nagini; Harry destroyed the diadem and Tom Riddle's diary. So the Horcruxes were not immune to destruction at the hand of someone other than Voldemort. And as it ended up, Harry himself wasn't even a Horcrux, but rather just an unknowing host to a parasitic bit of Voldemort's soul.   Why was it 'essential' that Voldemort be the one to kill Harry in order for the piece of Voldemort's soul to die? How do I escape a backtick ` within in-line code in Markdown? How do I escape a backtick ` within a code block?  This is probably a duplicate, since I'm sure it's a common concern, but I can't find a question that addresses this specifically.  How do I write List'1 with the "1" character still in the code-text format? I need to construct a real function with is exactly $C^2$ (that is, it is continuous and two times differentiable but it is not three times differentiable) such that its first derivative never vanishes.  I tried  $x^5 \sin(\frac{1}{x}) + \exp(x)$  $x^{\frac{5}{2}} + \exp(x)$  ${|x|}^3 + \exp(x)$  all these functions are exactly $C^2$, but their first derivatives vanish in some point(s). :( So in the documentation for the DescribeFieldResult.getDefaultValue , it says:     Returns the default value for this field   There is a related method called getDefaultValueFormula whose description reads:     Returns the default value specified for this field if a formula is not used.   What is the difference between these methods? I have a field with a default value. When I call getDefaultValue, I get null. When I call getDefaultValueFormula, I get back "This is the default value" (with quotes). I don't understand why getDefaultValue returns null. How do I create a script file for terminal commands?