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Adobe Illustrator: strange behavior while aligning objects states that the isomorphism type of a finite simple group is determined by its order, except that:   $L_4(2)$ and $L_3(4)$ both have order $20160$ $O_{2n+1}(q)$ and $S_{2n}(q)$ have the same order for $q$ odd, $n &gt; 2$   I think this means that for each integer $g$, there are $0$, $1$ or $2$ simple groups of order $g$.  Do we need the full strength of the  to prove this, or is there a simpler way of proving it? How can I test for a player wearing specific armor? How can I test for a player that is wearing an iron helmet named "test1" and an iron chestplate named "test2" in Minecraft Version 1.12? How to use induction to prove the product rule for higher derivatives? How do I show through mathematical induction that   \begin{equation} \frac{d^n}{dx^n}[f(x)\cdot g(x)] = \sum_{k = 0}^{n} \binom{n}{k} \frac{d^k}{dx^k} [f(x)] \cdot \frac{d^{n-k}}{dx^{n-k}} [g(x)] \end{equation}  which is the product rule for higher derivatives? Which is better: Employer-sponsored HSA or opening an HSA individually? So I know that:   Employer-sponsored HSA's allow you to deduct contributions directly from your paycheck, pre-tax With individual HSAs, you must contribute using post-tax dollars, then deduct those contributions from your taxable income when you do your taxes   Given those facts, I guess it's marginally better to use an employer-sponsored HSA because it means the government doesn't temporarily hold on to your taxed income, only to return it later after you do your taxes; you could theoretically put that money to work in an investment vehicle instead of having the government hold it hostage for a while.  But are there any other benefits (either way) that I'm not aware of? The  kind of threw me with the following statement:     The main advantage of making pre-tax contributions is the Federal Insurance Contributions Act tax (FICA) and Medicare Tax deduction, which amounts to a savings of 7.65% each to the employer and employee (subject to limits of the Social Security Wage Base).   But I'm not really sure what that's telling me.  My employer is offering an HSA, but is not offering to contribute to the HSA or match my contributions. So if it's all pretty much the same, I'd rather use the bank of my choosing and manage it privately.  Thanks. How do I "decompile" Java class files? What program can I use to decompile a class file? Will I actually get Java code, or is it just JVM assembly code?  On Java performance questions on this site I often see responses from people who have "decompiled" the Java class file to see how the compiler optimizes certain things. Show that if $f(z)=\sum\limits_{n\geq0}a_nz^n$ is analytic in $\{z\in\mathbb{C}:|z|&lt;1\}\cup\{1\}$ and $\forall n\geq0:a_n\geq0$ then the radius of convergence of the power series is strictly larger than $1$.  My approach:   Let $D=\{z\in\mathbb{C}:|z|\leq1\}$.  We have that $f(1)$ converges, so $\sum\limits_{n\geq 0} a_n&lt;\infty$. Moreover since the $a_n$'s are all positive we have that $|a_n|=a_n$, therefore $\sum\limits_{n\geq 0} |a_n|=\sum\limits_{n\geq 0} a_n&lt;\infty$.  Let $f_n(z)=a_nz^n$, then $\forall z\in D, n\geq 0$ we have:  $$|f_n(z)|=|a_nz^n|=|a_n|\cdot|z^n|=a_n\cdot |z|^n\leq a_n\cdot 1^n\leq a_n$$  Then, applying Weierstrass M-test we get that the power series is convergent in $D$.  Now, I need to "find" an open ball $B$ such that $D\subset B$ and the power series is convergent in it.  Edit  $f$ is analytic in $1$, so there is an open set $U$ that contains $1$ such that   $$f(z)=\sum\limits_{n\geq 0} b_n(z-1)^n$$  Does it mean that the series is convergent in $U$?   I can see that we have that the two series coincide in $D\cap U$. Why does Spring MVC respond with a 404 and report "No mapping found for HTTP request with URI [...] in DispatcherServlet"? Available US State or National business (or employer) database lists? This question dovetails with this post on .  I am familiar with some of larger, paid-for business registry's like  and .  While the detailed information their business listings database include (like # of employees, annual sales, industry code, etc) is fantastic, if you are on a limited budget, sometimes the cost of purchasing the data outweighs the value you can get from it.  If you have geocoding capabilities in house, one could potentially create a reasonable surrogate by spatially-enabling (geocoding) a publicly available business listing on your own.    If you were looking to take on this type of project, where would you start your research? Do you know of US agencies at a State or National level that maintain this type of information, AND are publicly available for download or minimal purchase? How do suggested edits work? What does: Error Broken count >0 mean? Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal? Is the ideal $I = \{f \mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on the interval $[0, 1]$ a maximal ideal? $pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes urlEvent is undefined Knife tool doesn't cut obscured edges I'm using Blender 2.66,  I find that the knife tool (K) doesn't work the way it used to.     Dragging across an obscured edge, even if selected, doesn't cut it. There seems to be no way to activate the option to do a midpoint cut or multiple cuts. How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure? I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure I did not get any of them. How can this be possible?  Here is the code:  fit5_snow&lt;- lm(Response ~ Stimulus, data=audio_snow) anova(fit5_snow)  &gt; anova(fit5_snow) Analysis of Variance Table  Response: Response           Df Sum Sq Mean Sq F value  Pr(&gt;F)   Stimulus   5  73.79 14.7578  2.6308 0.02929 * Residuals 84 471.20  5.6095                   --- Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1   df&lt;-df.residual(fit5_snow) MSerror&lt;-deviance(fit5_snow)/df  comparison &lt;-  HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)  &gt; comparison &lt;-  HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)  Study:  HSD Test for audio_snow$Response   Mean Square Error:  5.609524   audio_snow$Stimulus,  means                  audio_snow.Response   std.err replication snow_dry_leaves            4.933333 0.6208034          15 snow_gravel                6.866667 0.5679258          15 snow_metal                 6.333333 0.5662463          15 snow_sand                  6.733333 0.5114561          15 snow_snow                  7.333333 0.5989409          15 snow_wood                  5.066667 0.7713110          15  alpha: 0.05 ; Df Error: 84  Critical Value of Studentized Range: 4.124617   Comparison between treatments means                                Difference   pvalue sig        LCL      UCL snow_gravel - snow_dry_leaves  1.9333333 0.232848     -0.5889913 4.455658 snow_metal - snow_dry_leaves   1.4000000 0.588616     -1.1223246 3.922325 snow_sand - snow_dry_leaves    1.8000000 0.307012     -0.7223246 4.322325 snow_snow - snow_dry_leaves    2.4000000 0.071587   . -0.1223246 4.922325 snow_wood - snow_dry_leaves    0.1333333 0.999987     -2.3889913 2.655658 snow_gravel - snow_metal       0.5333333 0.989528     -1.9889913 3.055658 snow_gravel - snow_sand        0.1333333 0.999987     -2.3889913 2.655658 snow_snow - snow_gravel        0.4666667 0.994348     -2.0556579 2.988991 snow_gravel - snow_wood        1.8000000 0.307012     -0.7223246 4.322325 snow_sand - snow_metal         0.4000000 0.997266     -2.1223246 2.922325 snow_snow - snow_metal         1.0000000 0.855987     -1.5223246 3.522325 snow_metal - snow_wood         1.2666667 0.687424     -1.2556579 3.788991 snow_snow - snow_sand          0.6000000 0.982179     -1.9223246 3.122325 snow_sand - snow_wood          1.6666667 0.393171     -0.8556579 4.188991 snow_snow - snow_wood          2.2666667 0.103505     -0.2556579 4.788991 Finding CPU usage of a service Because my laptop fan was spinning up for no reason, I had a look at the CPU usage and I see  svchost with 12.5% CPU, which is basically a full core.  Now, I'm aware that  svchost runs services and I know how to display the services it runs in Task Manager or Process Explorer ().  Now I know which services are run, but I don't know which service eats the CPU time. I could disable one service after another, but I don't really like doing this (it could break things that are currently in use and I could forget turning the service back on later).  Therefore I'd like to know whether it's possible to instruct Windows to run only one service per svchost the next time I boot my PC. While I might have the slight disadvantage of several processes, I could immediately find out which one it is and it would be a much easier decision of whether or not to stop or restart the service. Lyman and Balmer series How to solve ~(P → Q) : P & ~Q by natural deduction? I'm trying to solve the following by natural deduction:  ~(P → Q) : P &amp; ~Q  It's a trivial problem if identities are used, as can be seen by the following:   {1}      1.   ~(P → Q)                    Prem. {1}      2.   ~(~P ∨ Q)                   1 Mat. Impl. {1}      3.   ~~P & ~Q                    2 De Morgan's {1}      4.   P & ~Q                      3 DNE   Starting from step 2 of the previous proof, it's also fairly straightforward to reach a conclusion using natural deduction; i.e. starting from ~(~P ∨ Q), which is an identity of ~(P → Q):  ~(~P ∨ Q) :  P &amp; ~Q   {1}      1.   ~(~P ∨ Q)                   Prem. {2}      2.   ~P                          Assum. {2}      3.   ~P ∨ Q                      2 ∨I {1,2}    4.   ~(~P ∨ Q) & (~P ∨ Q)        1,3 &I {1}      5.   P                           2,4 RAA {6}      6.   Q                           Assum. {6}      7.   ~P ∨ Q                      6 ∨I {1,6}    8.   ~(~P ∨ Q) & (~P ∨ Q)        1,7 &I {1}      9.   ~Q                          6,8 RAA {1}      10.  P & ~Q                      5,9 &I   I also found that it's fairly easy to conclude ~Q:   {1}      1.   ~(P → Q)                    Prem. {2}      2.   Q                           Assum. {3}      3.   P                           Assum. {2,3}    4.   P & Q                       2,3 &I {2,3}    5.   Q                           4 &E {2}      6.   P → Q                       3,5 CP {1,2}    7.   ~(P → Q) & (P → Q)          1,6 &I {1}      8.   ~Q                          2,7 RAA ... {1,2}    12.  P & ~Q   In spite of how easy it looks, I can't figure out how to do it. I believe it can be done in 12 steps. Thanks! How to book this complex multi carrier roundtrip flight I found on ITA? I am trying to book a roundtrip ticket from Chicago O'hare (ORD) to Mumbai, India (BOM). Traveling on Aug 9th and returning on Aug 24th. Now, I've been looking for several days (almost 10days!) for ways to book this itinerary I found on ITA. All other websites like Expedia, Kayak, Travelocity, Momondo, RouteHappy, and even google flights are quoting around $1200 roundtrip cost, sometimes as low as $1150. But the ITA Matrix website shows me several options, the lowest is $916 roundtrip.      You can see there are several flights in the $900 range.     For the return trip there is only one option to get the low price.  Selecting the flights this is what I get:      I'm not sure how to use the fare codes the ITA website provides to purchase this itinerary.  These are some of the things I have tried to book the complex multi-carrier flight from ITA:  My first method was to try coding into HIPMUNK, using the multi-city option, my departure, connections, airlines flights number and dates. Following this method:     And the results page:    Here's what my code into HIPMUNK looks like:  ORD::LH9151 FRA LH756 for the first journey and   BOM::LX155 ZRH SN5104 BRU SN8803 for the return trip.  Don't think I'm making any mistakes in coding it, but there are two adjustments I also made which failed:   I used the dates of the first leg of the flight then tried using the other dates as well. So for example Aug 9th and Aug 10th. I used the codes for the operating carriers and when it didn't work, the marketing carrier leaving the flight number unchanged.   This always returned no results. Breaking up the itinerary to just the oneway from ORD to BOM worked but gave me a price of $624. For some reason the second return trip was creating problems. I tried breaking he return trip down into different segments but no luck. Anyone knows why the return trip is creating difficulties? Coding issues/ hipmunk doesn't have such a large database?   Then I tried method 2: Calling up the airlines  United was able to find all the segments, even price it correctly sometimes (sometimes not) and gave me a confirmation number. I was to call them in 12hrs to check if they were able to procure the seats but when I did call they were not able to get the seats for the SWISS flight from BOM to ZRH and/or from ZRH to BRU. I've tried this at least 5 times changing small things everytime, but the same result. It seems Lufthansa waits for SWISS to confirm the seats but SWISS doesn't respond in time and I'm not able to book.  I tried calling Lufthansa but they were not even able to find the segments and instead told me to look at booking online where I will be able to find it cheaper.  Any insights into the methods that failed or suggestions on how to book this itinerary at the $900 price will be much appreciated. Thanks in advance.