Simple but hard 2 by 2 system in $x$ and $y$
Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$
Securely erase hard drive using the Disk Utility I am planning on selling my laptop. So I formatted my disk using the Disk Utility and chose to overwrite the disk with zeroes.  Two questions:  Is this the same as overwriting the disk using dd?  sudo dd if=/dev/zero of=/dev/sda   And is this method secure enough so that buyers can't easily recover the previous data? Or should I take additional measures (like encrypting the disk, destroying the headers, etc.)? I need a software, that emulates a printer, converts the printed documents to PDF/TIFF and send it via eMail to a specified address (for windows).  The virtual printer / PDF conversion is possible with a lot of PDF-converters. But I need a software, which is also able to directly mail me these PDFs. It's always the same mailaddress, and I have an SMTP server.  Any suggestions? Relation Between Bayesian Estimation and Maximum a posteriori estimation Is maximum a posteriori estimation some kind of Bayesian Estimation?   If yes, can you point out other Bayesian estimators?  Edit:  So I've come to know the following (don't know if they are correct):  MAP finds the mode of the posterior, and Bayesian Estimator finds the distribution of that posterior with respect to the estimating parameters. And in order for Bayesian Estimator to find the optimal parameters, some particular risk function (like Mean Squared Error, 0/1 error etc.) must be defined.  So it seems these two estimators have nothing in common except they both incorporate prior into their estimation. Or is it possible that MAP is some special case of Bayesian Estimator with some particular risk function. Particular nodes are missing from node editor I am looking for the  but it is not available under the Vector nodes menu or any other menu. I have Blender 2.77 which cooresponds with the manual version in the above link.    I also cannot find the Texture Coordinate or Gradient Texture.  Likely I am doing something wrong. If $A=AB-BA$, is $A$ nilpotent? Let matrix $A_{n\times n}$, be such that there exists a matrix $B$ for which $$AB-BA=A$$  Prove or disprove that there exists $m\in \mathbb N^{+}$such  $$A^m=0,$$  I know $$tr(A)=tr(AB)-tr(BA)=0$$ then I can't.Thank you Let $X$ be a non-negative random variable and $F_{X}$ the corresponding CDF. Show,   $$E(X) = \int_0^\infty (1-F_X (t)) \, dt$$   when $X$ has : a) a discrete distribution, b) a continuous distribution.   I assumed that for the case of a continuous distribution, since $F_X (t) = \mathbb{P}(X\leq t)$, then $1-F_X (t) = 1- \mathbb{P}(X\leq t) = \mathbb{P}(X&gt;  t)$. Although how useful integrating that is, I really have no idea. Is this a grammatically correct line in a poem: “Will he roll the dice, and follow it to Vegas?”? I want to use the following line in a poem: "Will he roll the dice, and follow it to Vegas?"   A couple of things to note; firstly, obviously I'm using "roll the dice" in both a figurative/idiomatic sense (as in taking a risk), and in a somewhat more literal sense (painting the image of the person actually following the dice that have been rolled to Las Vegas). That being said, my confusion here is if I can get away with using "follow it" or if I need to say "follow them" .... As I've read online "dice" traditionally refers to more than one die (i.e., the plural of die), but in the modern usage, "dice" can also be used to refer to the singular (i.e., just one die).   So, it seems like if I was referring to the image of just one die, then the way I phrased it could be correct. However, the image I'm trying to paint is the one usually associated with the phrase "roll the dice" (i.e., rolling two dice)...   So could "follow it" still be considered acceptable in this sense... or would I need to use "follow them"?... And if not referring to the dice themselves, could using, could the "it" be taken to refer to the act of rolling the dice, or would that not work either? Thanks so much in advance!! I want to get random decimal digits out of a 6-faced die.  Let's say the die is fair, with an equal probability for each outcome. (But feel free to share any consequences of that not being true, if you feel like it.)  I will represent the outcome of a die roll as a base-6 number:   In base-6 there are only 6 possible digits: $\{0,1,2,3,4,5\}$. The die has faces numbered 1 to 6. Face $f$ corresponds to digit $f-1$.   Thus, I can represent as many die rolls as I like with a base-6 number:   If the die is rolled once:   Let's say the die stopped on face $5$. The final base-6 number will be $4$.  If the die is rolled twice:   Let's say the die stopped on face $5$. And then on face $3$. The final base-6 number will be $42$.  If I roll the dice 10 times:   Let's say the die stopped sequentially on faces $5$, $3$, $4$, $6$, $2$, $3$, $3$, $3$, $2$, and $4$. The final base-6 number will be $4235122213$.    Since I want decimal digits, I need to convert to base-10.   Base-6: $4235122213$ Base-10: $44753985$   For any given number of die rolls, how many different combinations exist? If there are $r$ die rolls, the total of possible combinations is $6^r$.   $r$ rolls — $6^r$ different combinations. $0$ rolls — only $1$ combination. $1$ roll — $6$ different combinations. $2$ rolls — $36$ different combinations. $3$ rolls — $216$ different combinations. $4$ rolls — $1296$ different combinations. $5$ rolls — $7776$ different combinations. $6$ rolls — $46656$ different combinations. $7$ rolls — $279936$ different combinations. $8$ rolls — $1679616$ different combinations. $9$ rolls — $10077696$ different combinations.   $n_r$ ($\in \mathbb{N_0}$) is the number obtained after $r$ die rolls through the process described previously: "If the die is rolled once, twice, ..."  It is impossible for $n_r$ to reach the number of possible different combinations ($6^r$). It will be always short by least $1$:  $$ 0 \leqslant n_r &lt; 6^r $$   $r$ rolls — $n_r$ never surpasses $6^r-1$. $0$ rolls — $n_r$ never surpasses $0$. $1$ roll — $n_r$ never surpasses $5$. $2$ rolls — $n_r$ never surpasses $35$. $3$ rolls — $n_r$ never surpasses $215$. $4$ rolls — $n_r$ never surpasses $1295$. $5$ rolls — $n_r$ never surpasses $7775$. $6$ rolls — $n_r$ never surpasses $46655$. $7$ rolls — $n_r$ never surpasses $279935$. $8$ rolls — $n_r$ never surpasses $1679615$. $9$ rolls — $n_r$ never surpasses $10077695$.   I can never trust the leftmost nor the rightmost digit (fringe digits), since the possible values are potentially restricted.   For $0$ rolls, the outcome is always $0$. For $1$ roll, the fringe digit never surpasses $5$. For $2$ rolls, the leftmost digit never surpasses $3$, and the rightmost, $5$. For $3$ rolls, the leftmost digit never surpasses $2$, and the rightmost, $5$. For $4$ rolls, the leftmost digit never surpasses $1$, and the rightmost, $5$. For $5$ rolls, the leftmost digit never surpasses $7$, and the rightmost, $5$. For $6$ rolls, the leftmost digit never surpasses $4$, and the rightmost, $5$. For $7$ rolls, the leftmost digit never surpasses $2$, and the rightmost, $5$. For $8$ rolls, the leftmost digit never surpasses $1$, and the rightmost, $5$. For $9$ rolls, the leftmost digit never surpasses $1$, and the rightmost, $5$.   The other digits seem perfectly random to me though. Am I wrong? Proof that a sum of Bernoulli rvs has Binomial distribution Finding the Mobius Transformation that maps open unit disk onto itself Hi I am trying to find all the Mobius transformations that map unit open disk onto itself i.e., if $|z|&lt;1$ then $|f(z)|&lt;1$ where $f(z)=\frac{az+b}{cz+d}$. I did so far \begin{align*} &amp;\Big|\frac{az+b}{cz+d}\Big|&lt;1\\ \Rightarrow &amp; |az+b|&lt;|cz+d|\\ \Rightarrow &amp; |az+b|^2&lt;|cz+d|^2\\ \Rightarrow &amp; |az+b||\bar{a}\bar{z}+\bar{b}|&lt;|cz+d||\bar{c}\bar{z}+\bar{d}|\\ \Rightarrow &amp; |a|^2|z|^2+|b|^2+2\text{Re }(az\bar{b})&lt;|c|^2|z|^2+|d|^2+2\text{Re }(cz\bar{d}) \end{align*}   After that I am stuck. Can anyone help me. I would be obliged...Thanks in advance. Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module SFDX Pull error: Entity of type 'ListView' named XXX cannot be found While trying to pull changes from a scratch org (sfdx force:source:pull, tried with and without -f), I'm getting this error:     Entity of type 'ListView' named 'Note_Relation__c.My_Notes' cannot be found.   I do have a custom object Note_Relation__c, and it exists both locally and in the scratch org.  However, it's not an object that is normally accessed directly.  It has no tab, and should have no list views.  Nonetheless, I've checked the object's list view (via prefix, e.g., /a0D in both Classic and LEX view), and I can find no list views at all.  I've also tried adding an entry to .forceignore:  force-app/main/default/objects/Note_Relation__c/listViews/My_Notes.listView   This has no effect either.  At this point, I'm stuck with a bunch of config changes in a scratch org that I cannot pull.  I can find no references to this error message with scratch orgs.  Has anyone seen this issue?  Edit to clarify: I tried the .forceignore line based on what I think the file name should be; I have no force-app/main/default/objects/Note_Relation__c/listViews directory locally.  Edit 2: Workaround:  I found a workaround that doesn't make sense to me, but it works.  I'm not adding it as an answer yet because I'm not sure what's happening.  The workaround is to add the following line to .forceignore  Note_Relation__c.My_Notes   Even though this isn't a DX filepath, it's the name from the error message, and it seems to work. Most efficient way to check for DBNull and then assign to a variable? This question comes up occasionally, but I haven't seen a satisfactory answer.  A typical pattern is (row is a DataRow):   if (row["value"] != DBNull.Value)  {       someObject.Member = row["value"];  }   My first question is which is more efficient (I've flipped the condition):    row["value"] == DBNull.Value; // Or   row["value"] is DBNull; // Or   row["value"].GetType() == typeof(DBNull) // Or... any suggestions?    indicates that .GetType() should be faster, but maybe the compiler knows a few tricks I don't?  Second question, is it worth caching the value of row["value"] or does the compiler optimize the indexer away anyway?  For example:    object valueHolder;   if (DBNull.Value == (valueHolder = row["value"])) {}   Notes:   row["value"] exists. I don't know the column index of the column (hence the column name lookup). I'm asking specifically about checking for DBNull and then assignment (not about premature optimization, etc.).   I benchmarked a few scenarios (time in seconds, 10,000,000 trials):  row["value"] == DBNull.Value: 00:00:01.5478995 row["value"] is DBNull: 00:00:01.6306578 row["value"].GetType() == typeof(DBNull): 00:00:02.0138757   Object.ReferenceEquals has the same performance as "=="  The most interesting result? If you mismatch the name of the column by case (for example, "Value" instead of "value", it takes roughly ten times longer (for a string):  row["Value"] == DBNull.Value: 00:00:12.2792374   The moral of the story seems to be that if you can't look up a column by its index, then ensure that the column name you feed to the indexer matches the DataColumn's name exactly.  Caching the value also appears to be nearly twice as fast:  No Caching: 00:00:03.0996622 With Caching: 00:00:01.5659920   So the most efficient method seems to be:   object temp;  string variable;  if (DBNull.Value != (temp = row["value"]))  {       variable = temp.ToString();  } Reflection of sound waves from the open end of an organ pipe & relationship b/w nodes & pressure We know that standing waves are created when any wave traveling along the medium will reflect back when they reach the end. But in an open organ pipe, there is nothing to oppose the wave and reflect it back. So then how are standing waves created in such a case? In standing waves where is the pressure greater, at nodes or anti-nodes? Does a controlled mount share its rider's turn? From "Controlling a Mount" on p.198 of the Player's Handbook:     The initiative of a controlled mount changes to match yours when you mount it. It moves as you direct it, and it has only three action options; Dash, Disengage, and Dodge. A controlled mount can move and act even on the turn that you mount it.   Does this mean that the rider and mount share a single turn? Tsunami dampening mechanisms Encouraged by the zeitgeist let me ask the following:  Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it reaches the coast itself?  The following picture comes to mind. We have some device which is small enough to be mounted on a buoy. An array of such buoys can be anchored some distance off the coastline, controlled by computers which are linked into the global tsunami warning network. This setup is quite feasible given what a cell phone can do today.  On the detection of an oceanic earthquake or other tsunami generating event (such as a piece of the Rock of Gibraltar falling into the sea) and given present environmental conditions one can calculate the expected path of the tsunami and its intensity. If a TDS (Tsunami Dampening System) of the type I describe above happens to be deployed in range of the tsunami, all relevant information is conveyed to the TDS controllers by the global tsunami warning system. All this happen in a matter of moments.  This leaves plenty of time (25min - 2hr) for the devices in the TDS array to be activated and to do their job. The question in this case would be - what form could such devices take? Perhaps mini-turbines which could dissipate the incoming energy into the ocean by first converting it to electrical energy.  Any such undertaking involves physical estimates for the size and shape of such an array, the precise capabilities of each device, etc. Many of these concerns involve simple physical questions.  Can you come up with the details of such a system or alternatively outline your own design? If you think that this idea would never work in the first place - for technological, physical or some other reasons - please explain what you think would be the prime obstacle and why? Add a list of questions selected for HNQ to the 10k tools Now that questions selected for Hot Network Questions have a record attached to them, those can be queried for in the Data Explorer. However, the Data Explorer is only updated once a week. It would be nice to also have a full list of questions that are selected for Hot Network Questions and the times they were selected added to the 10k tools. In my opinion, it adds to the &quot;bird's eye view&quot; of the site that is afforded to them, and is in line with other similar lists (e.g. migrated questions, protected questions, etc.). Also, a list of questions that were removed from Hot Network Questions by a moderator would be very nice as well. How do people understand astromech droids? Is indefinite integration non-linear? Warning when battery is fully charged I would like to get an alert (with sound) when my laptop battery is fully charged.  How can I do that?