How do I determine the levels for some NPCs I'm building to fight the player characters?
If I design a PC for use as an NPC, how much XP should he give when killed?
I ran into the problem that my primary key sequence is not in sync with my table rows.   That is, when I insert a new row I get a duplicate key error because the sequence implied in the serial datatype returns a number that already exists.  It seems to be caused by import/restores not maintaining the sequence properly. Effective Refractive Index in Paper I am reading the paper, entitled "Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings" by Eric B. Grann, M. G. Moharam, and Drew A. Pommet.   In the paper they mention this formula:        Do you know how it can be derived and where it comes from ? Login failed for user - Error 18456 - Severity 14, State 38 Why does a circle enclose the largest area? How to compute $k$'th roots $\!\bmod n$? I have the following equation: $$ n \equiv M^k\mod(b) $$ where n, a, b are integers, and M is unknown. How do I solve this equation to find the M value? Those a and b are public keys of the RSA algorithm and n is the result of encryption. I need to find the encrypted message. Donating winning lottery ticket to 501(c)3 Private Foundation: cost-basis deduction + full tax free redemption for foundation? US 501(c)3 Private Foundations are typically controlled by the primary donator, so that is a nice perk, but in exchange for that perk I realize the tax deductions for donating are significantly lowered than for charities. Aside from being lower, the tax code doesn't recognize appreciated property and only allows for a deduction based on the donating taxpayer's cost-basis: ie. the price they paid for the property no matter its current market value.  When there is a significant delta of price paid vs current redeemable value, it seems this can still be a perk for the donating taxpayer in some circumstances, such as with lottery tickets that are known winners already.  If the donating taxpayer pays $1 for the ticket. Their cost basis is $1. If the ticket is now worth $100,000,000 but has not been redeemed, is it accurate that the donating taxpayer can donate this to their private foundation for a deduction at cost basis, and the private foundation can redeem the $100,000,000 ticket completely exempt from all lottery withholding income taxes?   (Other taxes unique to private foundations are known and outside the scope of this question.)  Most literature I can find is about appreciated marketable securities, and occasionally real estate. It doesn't seem that the tax code specifies any distinction between property, but it also doesn't seem the answer to this question is part of the general collective conscious even if it really is that obvious if my understanding is already correct. Can you cast a spell learned from the Magic Initiate feat using spell slots? Can you cast a spell learned from the Magic Initiate feat using spell slots? Say I play a wizard who learns cure wounds by taking the Magic Initiate feat. Could I cast that spell using the Wizard's spell slots? Fibonacci sequence and Euclidean algorithm's connection. Let $f_1, f_2,\dots,f_i,\dots$ be the Fibonacci sequence with $f_1=f_2=1$. For any $a,b\in\mathbb{N}$ with $a&lt;b$, suppose the Euclidean algorithm takes $n$ long divisions to compute $\gcd(a,b)$. If $a\le f_j$, then $n\le j-1$, for $j\ge2$.   I want to prove this problem. But I can't see any connection between Fibonacci and Euclidean algorithm. If anyone can give a hint about first step, it will be very thankful.  My guess is to use induction. Dini's Theorem - Proof. I'd like to prove the following:  If $f_j$ are continuous functions on a compact set $K$, and $f_{1}(x) \leq f_{2}(x) \leq \dots$ for all $x \in K$, and the $f_j$ converge pointwise to a continuous function $f$ on $K$ then in fact the $f_j$ converge uniformly to $f$ on $K$.  Attempt:  Let $g_{j}(x) = f(x) - f_{j}(x)$ for all $j$. Then, since $f_j \rightarrow f$ pointwise, we see $g_j \rightarrow 0$ pointwise.  Now, let $\varepsilon &gt; 0$ . And examine { $x \in K : g_{j}(x) &lt; \varepsilon$ }.  I've been told that the next step should be to  show that { $x \in K : g_{j}(x) &lt; \varepsilon$ } is equal to the intersection of $K$ with some open set $U_j$. But I'm not certain why this is true?   Advice? Insight? I have a .txt file with numbers ordered like this (on the same row):  106849_01373    106849_01967    106850_00082    23025.7_01059      I would like to convert them like that:  106849_01373 106849_01967 106850_00082 23025.7_01059   I have no idea which command to use. Can somebody help me with this? What’s the rule for using “who” and “whom” correctly? Make Google stop sending 'new sign in from ...' emails I get at least two emails from Google every time I sign in to my account and I want it to stop.  I tried changing the notification settings in Gmail, but they're still coming and they're useless.  How can I stop this? What is glue stretching? I had a question about dynamic vspaces () and there was a hint I should use a stretchable glue. Searching with Google didn't give me a helpful answer.  I would be glad, if someone can explain it and give me a simple example to understand how it works. Add Item to Finder Sidebar I am an international student in the US (important as my stay in US is tied to my student visa, issued to attend my current university).  I joined as a grad student in the MS CS program in one of the okayish public universities (ranked ~50 on QS/US news). I joined in Fall '18 and am still in my first semester. I took all the so-called "difficult" courses, but I find them very trivial (considering my undergrad was from a very good university). I am very disappointed with the curriculum and feel the coursework is not at all rigorous for a grad-school.  I might sound super arrogant, but I feel out-of-place when I talk to other students and hear them cringe about how hard the courses are, or how they don't have enough time to finish assignments within the deadlines as I find all of the coursework very trivial and feel that the assignments are a joke.   Fortunately, I am working with one of the best profs the university has to offer on a very impactful project and the research is going great. But that's the only plus point I see from sticking around.  My aim from grad school is to get research experience and join one of the Big 4s or upcoming CS unicorn startups. I cannot see myself joining one of the Big-Ns after graduating since the students from this school rarely bag a Google/Fb/unicorn startup job.  Since December is the Fall'19 admissions deadline, I am thinking about reapplying to those top 10 CS schools which I couldn't get into last year (probably because of my poor undergrad GPA).   On the other hand, since every CS company just asks leetcode-style questions in interviews, I can just be super good at it and try to nail whatever interview I get without wasting another year and then doing the same.  I'm not really interested in any kind of credit transfer either since I would like to start fresh in a more rigorous curriculum.  I'm not sure if switching schools would be a wise decision and could really use some advice from the community here.  PS :  Probably related -   Posting with a dummy account for anonymity. MySQL Seems to be crashing quite often, I'd say every hour or so.   The only thing running on this server that is using MySQL is a Drupal installation that I'm working on, there's only one person that's using it and it literally has around three pages - from what I can gather this seems to be a memory issue with innoDB? I'm not great at this stuff so I'm unsure.  Any guidance? Here's the relevant parts from my error.log  140216 14:20:01 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:01 InnoDB: The InnoDB memory heap is disabled 140216 14:20:01 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:01 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:01 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:01 InnoDB: Completed initialization of buffer pool 140216 14:20:01 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:01 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:01 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:01 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:01 [ERROR] Aborting  140216 14:20:01 [Note] /usr/sbin/mysqld: Shutdown complete  140216 14:20:02 [Note] Plugin 'FEDERATED' is disabled. 140216 14:20:02 InnoDB: The InnoDB memory heap is disabled 140216 14:20:02 InnoDB: Mutexes and rw_locks use GCC atomic builtins 140216 14:20:02 InnoDB: Compressed tables use zlib 1.2.3.4 140216 14:20:02 InnoDB: Initializing buffer pool, size = 128.0M InnoDB: mmap(135987200 bytes) failed; errno 12 140216 14:20:02 InnoDB: Completed initialization of buffer pool 140216 14:20:02 InnoDB: Fatal error: cannot allocate memory for the buffer pool 140216 14:20:02 [ERROR] Plugin 'InnoDB' init function returned error. 140216 14:20:02 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed. 140216 14:20:02 [ERROR] Unknown/unsupported storage engine: InnoDB 140216 14:20:02 [ERROR] Aborting  140216 14:20:02 [Note] /usr/sbin/mysqld: Shutdown complete   EDIT The server is the lowest-spec DigitalOcean Droplet with 512MB RAM. This particular Droplet is running NodeJS, MySQL and Apache. There's a low-traffic static site, a Ghost blog and this Drupal site I'm developing.   Should I just upgrade the RAM, or is there something I can do to fix this? Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$ Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? Process substitution and pipe I was wondering how to understand the following:     Piping the stdout of a command into the stdin of another is a powerful   technique. But, what if you need to pipe the stdout of multiple   commands? This is where process substitution comes in.   In other words, can process substitution  do whatever pipe can do?   What can process substitution do, but pipe cannot? Footnotes in tables? I would like to have footnotes in tables, but the \footnote command does not work inside a table environment.  Googling one finds that this is , at least in the UK.  That link contains a list of solutions to the problem, but since the author of the FAQ does not believe that this is good style, no comparison is made between the different methods.  I am sure that there are good typographical reasons why in most situations it is undesirable to have footnotes in tables (although I have never come across them), however I have recently felt the need to do just this in a paper I am currently writing.  Therefore I'd like to ask two questions:   What are the arguments against footnotes in tables? If one really must go against the advice in 1., which method (whether considered in the  or not) would you recommend?   Thanks in advance.  Added  In response to ShreevatsaR's comment: I do not much care for where the text of the footnote appears.  I do however insist on the footnote marks being attached to the relevant entries in the table, so that I can avoid having to reference "the second entry in the eighth line of the table", etc... Is a "split plot" ANOVA with two factors the same as two-way ANOVA with repeated measures in one factor? Is a "split plot" ANOVA with two factors identical to two-way ANOVA with repeated measures in one factor? if not, what is the distinction?