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Short story - "One man's meat is another man's poison" I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization. JavaScript variable definition: Commas vs. Semicolons Series $\frac{x^{3n}}{(3n)!} $ find sum using differentiation how to host multiple pages from diferent domains all together? Bound for the correlation of three random variables Cyclic orbit animation I'm trying to make one object orbit another. But I want it to repeat, rather than stop at 100 frames. It seems there is no option for this. Is there a way to make this happen? How to change an application Icon Possible Duplicate:          The square root of a number squared is equal to the absolute value of that number. Why is $\sqrt{x^2} = |x|$? Why not just $x$? Please give me a reason and also help me prove it. I need to delete some rows from one large table. The rows to delete shouldn't be in another table, example:  DELETE FROM LargeTable WHERE id IS NOT IN (SELECT DISTINCT foreign_id from EvenLargerTable)  but my server can't handle such blunt query, because there are almost a million records in the LargeTable and few million records in the EvenLargerTable  How can I solve it? Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$? Let $R$ be a commutative ring with 1, we define  $$N(R):=\{ a\in R \mid  \exists k\in \mathbb{N}:a^k=0\}$$  and  $$U(R):=\{ a\in R \mid a\mbox{ is invertible} \}.$$  Could anyone help me prove that if $a\in N(R) \Rightarrow 1+a\in U(R)$?  I've been trying to construst a $b$ such that $ab=1$ rather than doing it by contradiction, as I don't see how you could go about doing that. How to address a professor in letter? Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist. Winter Bash 2019 bugs with the "glasses with a number on top" hat and the "Philanthropist" hat Conditional expection of gamma distribution on sum I have a process which consists of a number of events and what is known is the timings between the events. What I'm trying to determine is a distribution that allows me to determine a likelyhood that a new sample fits the distibution.  The issue is mainly that if you have lots of samples you can approximate the result using a standard gaussian and use the mean and standard deviation. But if you only have a handful of samples, the gaussian does not accurately represent the situation.  From what I've read it is common to model waiting times using the gamma distribution. Looking at how the process evolves it looks like it matches well. The unknown is the scale parameter, since the shape parameter I think should be the number of samples. What I've worked out so far is that given the timings $X_1 ... X_N$ you can say:  $$ \sum_{n=1}^N X_n \sim \Gamma(N,\theta) $$  ($N$ is known and fixed)  However, $\theta$ is unknown, but the maximum likelihood parameter is the average of the $X_i$ (according to wikipedia anyway).   My question is, can I use this to estimate a distribution for $X_i$, that is, since the $X_i$ are independent:  $$ N X_i | \sum_n X_n \sim \Gamma(N, \tfrac{1}{N}\sum_n X_n) $$  Something else I've wondered about. Suppose I do have information about $\theta$, say a distribution. How can I incorporate this into the model?  Edit: Clarified that N is fixed. Convergence of cos, sin, tan functions In Radian mode, continually pressing the $\cos$ function of a number causes the result to converge to $x=0.739085133$, a fixed point of $\cos(x)$. Repeating this behavior with the $\sin$ function causes the result to converge to $x=0$, a fixed point of $\sin(x)$.   What happens if this is done using the tan function? It seems that $x=0$ is a repelling fixed point with no convergence in this case.  What would be the best way to explain these results mathematically? link new object to scene with python in 2.8 I understand that for resistors in series we need to add R for each resistor to get the equivalent resistance, where R is resistance. I also understand the mathematical manipulations that show that for resistors in parallel we need to add the 1/R for each resistor to get the equivalent resistance. However I have a couple of questions that have to do with the physical interpretation of the mathematical manipulations involved.   First, I am trying to understand why in the case of parallel resistors we have to add 1/R's instead of adding R's as in the case of resistors in series i.e. could it be thought that the current in the wire is like a sort of water flow in the pipe that has two horizontal parallel pipes positioned one on top of the other and in between connected by a number of vertical pipes that have a tap each that could be adjusted to represent different resistances. Then at the top of each vertical pipe the water pressure P exists and at the bottom the pressure will be reduced by P*R.   For example, suppose we have three vertical pipes, so then the pressure at the bottom of each (after the tap) is P*R for the total of 3*P*R so why is the equivalent resistance not 3*R*P but 1/R = (1/R1 + 1/R2 + 1/R3) and how can I be able to visualize this relation? Why am I getting zero divergence of function $\vec{f} = \frac{1}{r^2} \hat{r}$, where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of this function over a sphere of radius $R$, which includes the origin.  $$\nabla \cdot f = \frac{1}{r^2} \frac{\partial}{\partial r}(r^2 f_r) = \frac{1}{r^2} \frac{\partial}{\partial r}(r^2 \frac{1}{r^2}) = 0$$ We have an instance of SQL Server 2008 installed on a customer server. The customer's IT department is in charge of the various backups of the machine.  The SQL Server log shows there is a full backup every day at 7 PM but we can't find evidence of any plan scheduled in SQL Server.  The technicians we contacted couldn't tell us if there was some sort of automatic backup, all they told is that the entire machine is being backup up.  Using a script I found in  I found out that the physical device name is a GUID and that this means that this is an external backup process:  USE [msdb] GO  SELECT      [bs].[database_name],      [bs].[backup_start_date],      [bs].[backup_finish_date],      [bs].Server_name,     [bs].user_name AS [BackupCreator] ,     [bmf].physical_device_name FROM msdb..backupset bs   INNER JOIN msdb..backupmediafamily bmf ON [bs].[media_set_id] = [bmf].[media_set_id]  ORDER BY [bs].[backup_start_date] DESC   This is a row from the above query:     db_name 2015-09-16 19:01:23.000   2015-09-16 19:01:28.000SERVER_NAME  NT AUTHORITY\SYSTEM{424F084A-F35D-4A66-8FC7-072268A89A77} 5   Moreover the backup start and finish date spans only for 5 seconds, so I guess it's clear it's not a job of sql server.  This is a line from the log:     2015-09-03 19:02:30.71 Backup   Database backed up.   Database: db_name, creation date(time): 2012/10/12(20:52:11), pages dumped: 3290021,   first LSN: 276028:152755:172, last LSN: 276028:152827:1, number of dump devices: 1,   device information:   (FILE=1, TYPE=VIRTUAL_DEVICE: {'{95380B0A-D50B-408F-B95F-1AB8975BA7F8}5'}).   This is an informational message only. No user action is required.   So, since they can't help us what can I do to track down the process responsible of the backups? We need this because we want to coordinate the backup in an ordered manner, and do the transaction log backups too in order to keep the log at a reasonable size (now we do shrink the log every week, and this is not the good way to go).