How many square numbers exist that have the length $N$ in the decimal system?
What do you call the grouping of numbers based on the cardinality of digits in the square they produce?
I can't seem to access instance members of the surrounding class from inside an enum, as I could from inside an inner class. Does that mean enums are static? Is there any access to the scope of the surrounding class's instance, or do I have to pass the instance into the enum's method where I need it?  public class Universe {     public final int theAnswer;      public enum Planet {         // ...         EARTH(...);         // ...          // ... constructor etc.          public int deepThought() {             // -&gt; "No enclosing instance of type 'Universe' is accessible in this scope"             return Universe.this.theAnswer;         }     }      public Universe(int locallyUniversalAnswer) {         this.theAnswer = locallyUniversalAnswer;     } } There is a problem 3.3 in :     Ambiguities in the energy-momentum tensor:      (a) If you add a total derivative to Lagrangian ${\cal{L}} \rightarrow {\cal{L}} + \partial_\mu X^\mu$, how does the energy-momentum tensor change?      (b) Show that the total energy $Q = \int d^3x \; {\cal{T^{00}}}$ is invariant under such changes   Given the definition of energy-momentum tensor:  $$ {\cal{T}}^\mu{}_\nu = \sum_n \frac{\partial{\cal{L}}}{\partial \left( \partial_\mu \phi_n \right)} \partial_\nu \phi_n - g_{\mu\nu} {\cal{L}} $$  It changes as:  $$ \delta {\cal{T}}^\mu{}_\nu =  \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \left( \partial_\mu \phi_n \right)} \right) \partial_\nu \phi_n - g_{\mu\nu} {\partial_\rho X^\rho} $$  $T^{00}$ changes as:  $$ \delta {\cal{T}}^{00}= \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \dot{\phi_n}} \right) \dot{\phi_n} - \partial_\rho X^\rho $$   From this point I’m stuck. The first term doesn’t seem to disappear at all after integration over space, and the second disappears only partially:  $$ \int d^3x \; \dot{X^0} $$  So even if I’d have assumed that $X$ depends on position, and not on the fields - the total energy doesn’t seem to be invariant under it.  What is the best way to proceed forward with this? Determine whether a number is prime How do I determine if a number is prime?  I'm writing a program where a user inputs any integer and from that the program determines whether the number is prime, but how do I go about that? Given the differential equation $$\dot x = -2x + u$$ determine the optimal control law $u = - kx$ that minimizes the performance index $$J = \int_0^{\infty} x^2 \, \mathrm d t$$  My approach was to find the state feedback $k$. But since the value of $R$ (positive semidefinite Hermitian) is not given, that means $R=0$. How do I determine the optimal control for this system where $R=0$? Alternatives to one-way ANOVA for heteroskedastic data I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.  One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a  ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.   I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.  Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?  P.S.: my raw data are below:   A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432     0.494 0.719 B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897 C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958 I am working on setting up a Minecraft server on a machine I have at home. This particular machine has two quad-core CPUs running at 2.0Ghz so I would like to take advantage of the number of cores and run a server with 4 or 6 of the cores. My server of choice is CraftBukkit, the latest version of which is craftbukkit-1.4.7-R1.0 and launched with a start-up script of:  "C:\Program Files\Java\jre7\bin\java.exe" -Xms1G -Xmx8G -jar craftbukkit-1.4.7-R1.0.jar"   The  says:     Minecraft servers, as of 1.1.0, can use multiple cores, so now they will not sit idle.   but does not really expand on this.  My questions, then:   Is it possible to set the number of cores the server uses? How do I do it - via start-up options, or other methods? Is it really worth it and would it make that much of a difference with a lot of players? Prove: $\gcd(a,b) = \gcd(a, b + at)$. When does the Death Saving Throw happen with respect to sources of automatic ongoing damage? If a character is knocked unconscious with 0HP with a source of automatically dealt damage, for example, into a fire, and takes damage from it each turn, does the automatic Death Saving Throw failure from taking damage at 0hp happen before or after the player's regular Death Saving Throw roll?  If the unconscious PC takes the auto-fail first then they effectively only get 1 Death Saving Throw to survive, because they'd autofail and roll a failure the first turn, then autofail again and die the next turn.   If they get to roll first, then they only effectively get two death saving throws before they die. Why is my variable unaltered after I modify it inside of a function? - Asynchronous code reference When should "Mom" and "Dad" be capitalized? I am trying to understand capitalization rules with Mom and Dad. I believe I have it correct below, but please let me know if I do not.     The one thing I learned from my dad was that it was good to earn the trust of one's children. Dad has shown me how good that a dad can be. One day when I went to his house, and Dad wasn't there, I ran outside....   The above passage is just made-up just so that you would see what I mean about capitalization. Let's put numbers by each one, like so:     The one thing I learned from my dad(1) was that it was good to earn the trust of one's children. Dad(2) has shown me how good that a dad(3) can be. One day when I went to his house, and Dad(4) wasn't there, I ran outside....    This is one where I'm not certain. I believe in this sense I'm showing possession here with "my", and it just didn't seem right saying "my Dad". I don't know what the grammar rule is here, or if I even have it right. This one is obvious—it starts the sentence. In this case, I'm using Dad like a name instead of saying "Larry". Therefore, it should be capitalized. Again, just like 3. Map display not filling window in QGIS on Mac? Why absence of electron is called hole? How to properly unwrap my mesh? Is there a way to automatically unwrap my character? If not, is there a tutorial or something? My Father passed away - next test(s) on what remains of his DNA sample? I posted this general question over at the forum on FamilyTreeDNA. Though I received a reply, there is still no answer to my question, so I thought I'd try my luck at posting here.  Anyhow, in early 2009 I bought two kits for the Genographic Project and dutifully had my father do his cheek swabs: one kit for his Y-Chromosome, and one for his mtDNA. Once that was completed, I had his samples transferred to Family Tree DNA.  Then, late in 2009 I paid to have an mtFullSequence done on his mtDNA sample.  My father passed away in 2015. In early 2016, I phoned FTNDA to discuss. The first thing they did was arrange to merge his two original samples into one kit. Then, they suggested doing Family Finder. I did that and recently obtained the interesting results.  So, all told what I have done on my father is:   Y-12 (originally done for the Genographic Project) mtFullSequence Family Finder   My father's Y Haplogroup is R-M269 and I am being presented with the M343 SNP pack on FTNDA.  My question is, what now? My father is gone so the sample that remains with FTDNA is old and finite (their customer service says they still have "one container" of his DNA). His siblings have all passed away -- unfortunately, with no samples taken. What is the best way to make use of the sample of my father's DNA that is left?  Should I refine the Y-Chromosome to Y-111? That seems the most natural (though I'm a male and carry it too). Should any SNP tests best be done on his remaining sample as opposed to on me? Or, should I do nothing and just let his 2009 samples continue to sit at FTDNA?  By phone, FTDNA said that they should have enough left to do the Y-111 and a SNP pack which is great, but I'd love to know independent of their customer service if that is the wisest way to make use of the remaining DNA sample which they have?  Full disclosure: I did have my father do 23andMe in 2010 and I did have his blood drawn and sent to a DNA Bank. I hope to never touch his banked DNA (except maybe to do a full sequence someday), but at least it does exist. My question now is solely how to best make use of my father's remaining sample at Family Tree DNA? Ksplice is an amazing software (or whatever it is). It changes the way kernel updates work: Instead of rebooting after an update, it patches memory, so you don't need to do anything. Basic photo editing on OS X Convert a string to an enum in C# What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse(&quot;Active&quot;);  but that isn't a valid code. When is R squared negative? My understanding is that $R^2$ cannot be negative as it is the square of R. However I ran a simple linear regression in SPSS with a single independent variable and a dependent variable. My SPSS output give me a negative value for $R^2$. If I was to calculate this by hand from R then $R^2$ would be  positive. What has SPSS done to calculate this as negative?   R=-.395 R squared =-.156 B (un-standardized)=-1261.611   Code I've used:  DATASET ACTIVATE DataSet1.  REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA             /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN             /DEPENDENT valueP /METHOD=ENTER ageP   I get a negative value. Can anyone explain what this means? How is Dru-Zod/General Zod still alive after this character died? Show path of a body of where it should go after linear impulse is applied I am making a game with Andengine and Box2D. I have a dynamic body and I apply linear impulse on the body to move it around when the user have touched the screen.  Now I want to show the path where the body will go when the user have touched. If you have played Angry Birds or Basket Ball Shoot or any other which have projectile motion with a path shown you will get my point. I want to show the white dots which are shown in those games.