Applying texture to a specific colour
How to mix three different shaders on the same material?
Evaluating limit (iterated sine function) The limit is   $$\lim_{x\rightarrow0} \frac{x-\sin_n(x)}{x^3},$$  where $\sin_n(x)$ is the $\sin(x)$ function composed with itself $n$ times:  $$\sin_n(x) = \sin(\sin(\dots \sin(x)))$$  For $n=1$ the limit is $\frac{1}{6}$, $n=2$, the limit is $\frac{1}{3}$ and so on.  Can we define a recurrent relation upon that given hypothesis? Also, how do I involve $n$ into calculation, because the final limit will depend on it?  Any suggestions on how to tackle this?  Thank you! What is tail call optimization? VMware Linux Server -- how can you tell if you are a vm or real hardware? An interesting question.  I have logged into a Linux (most likely SuSE) host.  Is there some way that I can tell programmatically that I am a VM host or not?    Also assume that the vmtools are not installed. When installing user applications, where do "best practices" suggest they be located? Occasionally I install applications manually, rather than using apt or another package manager.   What location (/usr/, /usr/local/, /opt/, /home/, etc.) is suggested by "best practices" for the installation of user applications? Clarification on Rayleigh scattering causing various sky colors (I know Rayleigh scattering isn't the only reason why the sky is blue but to simplify the question lets focus on that)  The commonly stated reason for why the sky is blue is that smaller wavelengths are scattered more easily off the molecules in the air. During the day, because the blue light is scattered more, the sky is illuminated more with that blue light and more reaches your eyes. However, during sunsets and sunrises, the light from the sun must travel a longer distance. The explanation I have found is that the blue light is scattered away and more of the longer wavelength reds and greens are available to reach your eyes to get those warmer colors, (red and green of course mixing to get yellows).   My question is that it seems like these explanations are conflicting. If the light at sunsets and sunrises travels more distance, why won't the blue light be scattered even more and thus illuminate the sky with blue light more than in the daylight? It confuses me that in one case the scattering of blue light causes the sky to be blue but then at sunset the scattering eliminates this color. Could I get some explanation on this? How do I find out what fonts are used in a document/picture? Is it possible to identify the font used in a specific document/picture?  Answers to this question should identify:   Possible methods to do this (perhaps one answer per method) and adequately describe how to use it (as opposed to merely stating it); Ways of finding the identified fonts, if possible (free or not); and Any prerequisites associated with the method used, if required (for example, "In order to use method X, your document has to be in format Y").   This question is meant as an FAQ, based on an . Its aim is to facilitate the community with the general procedures involved in font identification. Similar cases are solved on a per-usage basis on 's  tag. Two seasonal periods in ARIMA using R I'm currently using R to predict a time series with these instructions:  X &lt;- ts(datas, frequency=24) X.arima &lt;- Arima(X, order=c(2,1,0), seasonal=c(1,1,1)) pred &lt;- predict(X.arima, n.ahead=24) plot.ts(pred$pred)   As you can see I've data each hour, and I chose the seasonal period of 24 (one day).  I would like to improve my forecasting using an additional seasonal period in order to include the seasonal component of the week (seasonal length of 7*24=168 data)  Is there any method for this? How do you do it?  UPDATE: I've read  (your) blog page, maybe can I use the external regressors to simulate a second seasonal period? Insert missing dates within table I have a table with a column for ID, Date and Frequency of occurrence for that particular date and ID.  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-20      1 4     2014-05-18      6   I'm looking to insert the dates for each ID that aren't currently there (assuming that the date ranges from 2014-05-18 to 2014-05-20) and add a value of 0 in Frequency for those.  For example, you can see that  ID 1 has an observation for all three dates;  ID 2 is missing 2014-05-18 and 2014-05-19;   ID 3 is missing 2014-05-19;   ID 4 is missing 2014-05-19 and 2014-05-20.  Therefore, the output should look like this  ID    date          Frequency 1     2014-05-18      5 1     2014-05-19      4 1     2014-05-20      25 2     2014-05-18      0 2     2014-05-19      0 2     2014-05-20      7 3     2014-05-18      4 3     2014-05-19      0 3     2014-05-20      1 4     2014-05-18      6 4     2014-05-19      0 4     2014-05-20      0   I've attempted the following from . However, that will only add dates with 0 Frequency that aren't present throughout the entire table instead of on an ID level.   DECLARE @s DATE = '20140518', @e DATE = '20140520';  SELECT c.date, Frequency = COALESCE(a.Frequency,0) FROM dbo.Calendar AS c LEFT OUTER JOIN dbo.table AS a ON c.date = s.[date] WHERE c.d &gt;= @s AND c.d &lt; DATEADD(DAY, 1, @e); SQL Select Upcoming Birthdays I'm trying to write a stored procedure to select employees who have birthdays that are upcoming.    SELECT * FROM Employees WHERE Birthday &gt; @Today AND Birthday &lt; @Today + @NumDays  This will not work because the birth year is part of Birthday, so if my birthday was '09-18-1983' that will not fall between '09-18-2008' and '09-25-2008'.    Is there a way to ignore the year portion of date fields and just compare month/days?   This will be run every monday morning to alert managers of birthdays upcoming, so it possibly will span new years.    Here is the working solution that I ended up creating, thanks Kogus.    SELECT * FROM Employees  WHERE Cast(DATEDIFF(dd, birthdt, getDate()) / 365.25 as int)     - Cast(DATEDIFF(dd, birthdt, futureDate) / 365.25 as int)  &lt;&gt; 0 Is there a way to have Cycles skip rendering alpha? Vandermonde determinant for order 4 [Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot. How can all labels of a given type of node be restyled in Tikz?  Imagine that there are nodes of different styles, and that only the nodes of style X should have red labels. Is this possible without having to change all labels one by one of nodes of style X? Let $a,b,c\in\mathbb{R}^*_+$, $abc=1$.  How can i show that $\left(a-1+\frac{1}b\right)\left(b-1+\frac{1}c\right)\left(c-1+\frac{1}a\right)\leq1$ ?  I got $\left(ab-b+1\right)\left(bc-c+1\right)\left(ca-a+1\right)\leq abc=1$, but i can't go any further ...  If i expand it :   $2-ab-\frac{b}a-c-ac-\frac{a}c-b+2a+\frac{2}a-bc-\frac{c}b-a+2b+\frac{2}b+2c+\frac{2}c-4$  Which gives using $c=\frac{1}{ab}$ :   $5ab-\frac{b}a-\frac{1}{ab}-a^2b+\frac{1}a+b+\frac{1}b-2$ Let's say you have a few expressions like the following:  $$\begin{array}((x+17)^2 \\ x^2 + 34x + 289 \end{array} \\ 288 + \frac{x^2}{2} + \frac{x^2}{2} + 34x + 1 \\ [...] $$  You get the idea: there's an infinite number of ways of representing the same expression. The challenge is that my application is validating answers to math problems, input by math students practicing a certain concept. I'd like to make sure that whenever they submit an answer, the checker is completely insensitive to the issues of ordering, simplification, formatting etc. which would be plain frustrating. I'd also ideally like to support more than one variable such as x, y, z in the same expression.  What's a reliable way to check that two expressions are the same? The most brute force way I can think of would be to just plug a number into each variable of each expression and see what the result is.  I have a hunch however that there might be ways of getting false positives this way. That, and I might be either missing something really obvious about this, or there might be a better way of doing the comparison.  Would love to hear what you think. Should I let potential employers know I have a job offer? I've interviewed for a few positions, one of which has made me an offer.  I'm very pleased with the offer, but I prefer some of the other positions.  I have the luxury of being able to take a lot of time to decide whether or not I accept this offer, so I'm certain I will hear back (either positively or negatively) from the other positions before a decision is required for the offer I've received.  I'm trying to decide between two courses of action, and I want to choose the one that will best help my candidacy with the positions I've yet to hear from.  Plan 1 is to do nothing and simply wait to hear back from the other positions for which I've already interviewed.  Plan 2 is to be in touch with the other positions to let them know I have an offer, and ask where I stand with them.  Would Plan 2 make me a more desirable candidate with the other positions, as they might see my offer as further validation of my credentials?  Or, might initiating with the interviewers in this way be detrimental to my candidacy, perhaps making me seem pushy or self-centered?  If so, I would rather just wait for them to run their course of action (Plan 1).  As I've said, I have plenty of time, so I don't want impatience to hurt me.  If there is a good chance that my meddling will be detrimental, then I'd rather be hands-off here.  However, if it's more likely that informing the other interviewers of my offer will give me a boost, then I'd want to do so.  Thanks for any clarity you can provide!  Edit: For a bit more information and context, the position I've been offered is a non-academic research position that my advisor has described as "prestigious."  The other positions for which I've interviewed (and which I prefer) are mostly academic teaching-centered positions (visiting assistant professors, tenure-track at smaller four year institutions). Why can't I import a SVG file from Adobe Illustrator or Inkscape? What I get:  host:~ user$ cat example.txt some texthost:~ stas$   What I want to get:  host:~ user$ cat example.txt some text host:~ stas$   Is there a way I can make cat behave like this?  I'm using bash on Mac OS X. Can US citizens go to Cuba freely and vice versa after the recent diplomatic relation restoration? A recent full diplomatic relation restoration between the US and Cuba took place, does that mean that US citizens can go to Cuba freely and vice versa? Why do we make a distinction between derivatives and partial derivatives?