For questions, you can attract attention by offering a bounty.  Now let's say you worked hard and offered what you feel is a very good answer (possibly a lot better than the currently accepted answer) - problem is - no one's looking at it - especially if there are already many answers with up-votes and with an accepted answer.  Is there any way to attract attention to it?  EDIT:   Feature request: What if we could ask for moderator attention for good answers (as well) possibly for a cost of some points - after which the moderators could decide to either reject the claim that it is a very good answer or distinguish it in some way - if it is indeed a good answer...like for example to display it as the first answer or the like.
Earlier today I posted  which yielded a .  I'd like to attract attention to this answer in the hope that the answer will get upvoted, as a kind of reward for the quality of the answer.  Is there anything that I can do to achieve this?
What is the relationship between philosophy and science? While philosophy and science as held as separate disciplines (and often taught in completely different colleges within a university [i.e. College of Liberal Arts vs. College of Science]), it is patently clear that there is an immutable relationship between philosophy and science. Philosophy can often be seen as providing justification for particular scientific theories -- but why/how is this so?  In science:   A theory must have observable consequences that can be tested and be falsified.   Theories also must agree with previous theories in the domains where they had been successfully tested.   For example,  special relativity reduces to Newton mechanics in the domain of velocities much less than the speed of light.  In philosophy, while new theories must comply with existing theories, there is clearly much less testing/retesting.  So, how does philosophy fit into this framework while maintaining the rigor required for scientific inquiry?  Are there any examples of philosophical discussions that have significantly influenced or changed scientific theory? A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$ Let $A$ be a $4\times 4$ matrix over $\mathbb C$ such that $\operatorname{rank} A=2$ and $A^3=A^2\neq 0$  Suppose $A$ is not diagonalizable.  Then which one is true   $A^2=A\neq 0$ $\exists$ a vector $v$ such that $Av\neq 0$ but $A^2v= 0$ the characteristic polynomial of $A$ is $x^4-x^3$   My try:  If $A^2=A$ then minimal polynomial of $A$ has two distinct roots and hence $A$ is diagonalisable hence false. Since $A^3=A^2\neq 0$ so the characteristic roots of $A$ are $0,0,1$ Since rank of $A$ is $2$ $1$ must appear twice so the characteristic polynomial of $A=x^4-(0+0+1+1)x^3+(0.0.1+0.1.1+1.1.0+1.0.1)x^2+(0.0+0.1+1.1+...)x+(0.0.1.1)$ hence 3 is false  2 I am not sure Please find the error in my solution and don't refer it to some previous solution What is the proper name for a "river plot" visualisation In a famous plot, Charles Minard visualised the losses of the French Army in the Russian campaign of Napoleon:    (another nice example is  xkcd plot)  Is there a canonical name for this type of visualisation? I'm actually looking for an R package to create such plots, but I don't even know how to look for it.  EDIT:  As I could not find a good package in R do do this type of plots, I have created my own, called "riverplot" -- you can download it . Here is a simplified version of the above diagram:    And an example of what other diagrams can be created with the package: Check and fix SD card errors within Android itself? Can a parallel computer simulate a quantum computer? Is BQP inside NP? Are PPAs safe to add to my system and what are some "red flags" to watch out for? I see a lot of interesting programs out there that can only be obtained by adding a "PPA" to the system but, if I'm understanding correctly, we should stay within the official "repositories" for adding software to our system.   Is there any way for a novice to know if a "PPA" is safe or if it should be avoided? What tips should the user know about when dealing with a PPA?. Below is the text in the file:  Pseudo name=Apple Code=42B state=fault  Pseudo name=Prance Code=43B state=good   I need to grep for "42B" and get the output from the above text like:   Pseudo name=Apple Code=42B state=fault   Does anyone have idea on how to achieve this using grep/awk/sed? How can I import the configuration on a different site? I have this error when I try to import the config of an another site:     The staged configuration cannot be imported, because it originates   from a different site than this site. You can only synchronize   configuration between cloned instances of this site.   I have 10 customers, and I need to sync my site configuration with 10 different websites. The site UUID is a problem for sharing a configuration with a different website. Is there a solution? UK visa refusal For PLAB 2 I had applied for a visit visa (business) to appear for my PLAB 2 exam on 21 June 2019. I had to attend practice classes from an academy in Manchester for which I had attached the invitation letter; my duration was 15 days to prepare my exam in a better way. I had mentioned the cost of my trip to be £1500 and my brother sponsoring me for £3000 (my entire trip).   My rejection letter stated that I was going with my mother, when I had nowhere in my form or cover letter mentioned that I am going with my mother, because I was going alone. I had shown that my brother is my financial sponsor as I didnt have enough funds in my account. I had attested all the documents of my brother but somewhere in my form I made a mistake where I wrote the total money I have is £3000, but I had only £1200 in my account. I thought we had to write the total amount, so I put my brother's sponsor money, which was supposed to be £3000; he hadn't transferred it into my account, it was in his account only.  I made one more mistake in the form where they asked how much is the cost of travel to you personally. I wrote £1500 but I think I had to write nil there.   I don't know how to proceed now. Should I transfer £3000 into my account from my brother's account and get a bank statement proving the source of income? I don't have enough money in my account despite bring employed since Nov 2018 with a salary of £700 per month, as I had to make some big transactions such as booking my PLAB 2 exam (£830£), etc.  I have already booked the exam for £830 and I don't have much time left. Installing VMware on 18.04: Failed to build vmmon I have a project where I have a few layers (State of Texas, cities, roads, etc.). They are all resaved and projected to NAD83 / UTM zone 14N EPSG: 26914. The project CRS is also NAD83 / UTM zone 14N EPSG: 26914 and on the fly projection is enabled. I added a text delimited file and cannot get them to line up. I checked the attribute table of the delimited file and the coordinates are correct. I cross-checked this with a point close to where a few of the points from the delimited file are and they are very close so in theory they should be lining up. I tried to save the delimited file and save it with the same projection and add the shp file back in and that did not work. Anyone have any ideas? I can't think of anything else to try. Any ideas how to display a PDF file in a WPF Windows Application?     I am using the following code to run the browser but the Browser.Navigate method does not do anything!  WebBrowser browser = new WebBrowser(); browser.Navigate("http://www.google.com"); this.AddChild(browser); // this is the System.Windows.Window How to round a number to n decimal places in Java I've tried everything I can think of. Resetting the router, changing the channel number and band.   The internet connection is fine, and then just hangs for a minute or 2, then returns to normal.   The wifi icon remains connected, and I have the latest 10.10.4 update installed. At first I thought it was a DNS bug with Yosemite, and have played with the settings such as changing DNS provider, changing the IPV6 to IPV4 only etc.  Driving me nuts. Has anyone had a similar problem? I've checked the surroundings with wifi scanners and have chosen the best channel available.     One thing I have noticed, it seems a lot more reliable on 5GHz as opposed to 2.4Ghz It seems to affect my Macbook Pro Retina 13in Early 2015 a lot more than the other devices on the network. I'm using a Virginmedia  1. Is it possible record videos of my screen? Suppose that I would like to record some video sessions of Angry Birds on my phone.   Are there any apps that I can use? I have root permissions. I'm trying to prove that the converse of Lagrange's theorem is true for finite abelian groups (i.e. "given an abelian group $G$ of order $m$, for all positive divisors $n$ of $m$, $G$ has a subgroup of order $n$"). This is an exercise from a book, and it is in the section on finite abelian groups, so I know I have to use the fundamental theorem of finite abelian groups. I have come up with a proof, but it seems a bit messy, and I'm not entirely sure if it's correct. It is given below.     Let the order of $G$ be $m$ = $p_1^{\alpha_1} \ldots p_k^{\alpha_k}$. It is known that $G$ is a direct product of $p$-groups, say:      $$G = G_1 \times \ldots \times G_k$$      where each $G_i$ is a $p_i$-group. By the fundamental theorem of finite abelian groups, each $G_i$ is isomorphic to a direct product of cyclic groups of the form      $$\mathbb{Z}_{{p_i}^{\beta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\beta_l}},$$      where $\beta_1, \ldots, \beta_l$ are positive integers such that $\sum_{j=1}^l \beta_j = \alpha_i$. Now if $n$ divides $m$, then we must have      $$n = p_1^{\gamma_1} \ldots p_k^{\gamma_k}$$      for some $\gamma_1, \ldots, \gamma_k$ with $0 \leq \gamma_i \leq \alpha_i$.      Claim: Each $G_i$ has a subgroup of order $p_i^{\gamma_i}$      Proof: As above, we have that       $$ G_i \cong \mathbb{Z}_{{p_i}^{\beta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\beta_l}} $$      where $\beta_1, \ldots, \beta_l$ are positive integers such that $\sum_{j=1}^l \beta_j = \alpha_i$.      Now since $0 \leq \gamma_i \leq \alpha_i$, we can find   $l$ numbers $\delta_1, \ldots , \delta_l$ such that $\gamma_i = \sum_{j=1}^l \delta_j$, and $0 \leq \delta_j \leq \beta_j$. (This choice of numbers is not necessarily unique).      Then $p_i^{\delta_j} | p_i^{\beta_j}$ for each $j = 1, \ldots , l$. Hence, for each factor $\mathbb{Z}_{{p_i}^{\beta_j}}$, there exists a subgroup of order $p_i^{\delta_j}$, namely $\mathbb{Z}_{{p_i}^{\delta_j}}$ (using the fact that the converse of Lagrange's theorem is true for finite cyclic groups). Taking the direct product of each of these subgroups, we get a new subgroup $G_i'$ of $G_i$:      $$G_i' \cong \mathbb{Z}_{{p_i}^{\delta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\delta_l}}$$      The order of this subgroup is $p_i^{\delta_1} \times \ldots \times p_i^{\delta_l} = p_i^{\delta_1 + \ldots + \delta_l} = p_i^{\gamma_i} $. So we have found a subgroup of $G_i$ of order $p_i^{\gamma_i}$, as required.      So each factor $G_i$ in the product $G = G_1 \times \ldots \times G_k$ has a subgroup $G_i'$ of order $p_i^{\gamma_i}$.       Therefore, $G$ has a subgroup   $$G_1' \times G_2' \times \ldots \times G_k'$$       of order $p_1^{\gamma_i}...p_k^{\gamma_k} = n$, which completes the proof.   I have two questions about this: firstly, does this proof seem to work? Secondly, is there a way to make the proof more concise (e.g. a way to prove the statement without using all these indices)? Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$ I need to prove that $\sup \{-x \mid x \in A\} = -\inf\{x \mid x \in A\}$ and am having trouble moving the $-x$ out of the $\sup$ to $\inf$. Another thing is that I don't quite know how to prove $b = \inf$ (see below). Any help would be appreciated! Here my attempt:  Let $a = \sup\{-x \mid x \in A\}$  Then by definition $a \geq -x$ for $x \in A \implies -a\leq x$ for $x \in A$  Thus $-a$ is a lower bound of $A$. Assume $b$ is a lower bound of $A$  Then $b \leq -a \implies  a \geq -b$ and $a = \sup \{−x \mid x\in A\} = -\inf(A)$ Commutator Subgroup and the Largest Abelian Quotient Good day. I'm not too sure how I should go about asking my question, so if it is in anyway confusing, feel free to edit it.   In my Group Theory course we defined and showed a few properties of the commutator subgroup $[G,G]$ of a group $G$. And then we stated and proved a lemma in lecture that I'm having some difficulty wrapping my head around. I'll state it here for clarity.  Lemma a) The commutator subgroup $[G,G]$ of $G$ is a normal subgroup of $G$. b) The quotient group $G / [G,G]$ is the largest abelian quotient of G in the sense that every homomorphism $\varphi : G \to A$ where $A$ is an an abelian group, induces a unique homomorphism $\bar \varphi : G/[G,G] \to A$ so that $\varphi =\bar \varphi \circ \pi$ where $\pi : G \to G/[G,G]$ is the quotient homomorphism.  Now, it's not the proof of this lemma that I'm having trouble with, it's the italicized text that is messing with me. I completely understand what it is that the italicized text is saying, I'm just not too sure why it is that the property gives us the "largeness" that is claimed. I can see that the above forces $G$ to "pass through" $G/[G,G]$ before it "reaches" $A$ (I apologize for the casual terminology), so I can sort of see why $G/[G,G]$ should be the largest quotient, in a non-rigorous sort of way.  Overall I'm very confused. Perhaps I'm missing something very simple. Any help or nudges in the right direction would be much appreciated.   As a side note I did try a search on Google and here on Stack Exchange and couldn't find anything that answered my question. So if I missed something obvious, then my apologies. Thank you in advance. Input impedance of Arduino Uno analog pins? I'm using the  on some small robotic arm motors, and reading in the analog voltage with an Arduino Uno.  I've had reasonably good results, but only after putting in an RC filter on the output.  However, in the application note on the datasheet, it says not to do that:  "the addition of an RC filter to the output of a sensor IC can result in undesirable device output attenuation — even for DC signals."  Then it gives a formula to calculate attenuation, but it depends on knowing the input impedance of whatever is reading the signal, so that's what I'm after here. What is the name of the first decade in a century? 80s: the "Eighties"   90s: the "Nineties"   00s: the ???   For that matter, what is the second decade called? The "tens" just doesn't sound right.