How to bake muffins with a convection oven and steam
The muffins were rock hard, what did I do wrong?
The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through? Purely "algebraic" proof of Young's Inequality states that if $a, b \geq 0$, $p, q &gt; 0$, and $\frac{1}{p} + \frac{1}{q} = 1$, then $$ab\leq \frac{a^p}{p} + \frac{b^q}{q}$$ (with equality only when $a^p = b^q$).  Back when I was in my first course in real analysis, I was assigned this as homework, but I couldn't figure it out.  I kept trying to manipulate the expressions algebraically, and I couldn't get anywhere.  But every proof that I've seen since uses calculus in some way to prove this.  For example, a common proof is based on this  and integration.  The proof on Wikipedia uses the fact that $\log$ is concave, which I believe requires the analytic definition of the logarithm to prove (correct me if I'm wrong).  Can this be proven using just algebraic manipulations?  I know that that is a somewhat vague question, because "algebraic" is not well-defined, but I'm not sure how to make it more rigorous. But for example, the proof when $p = q = 2$ is something I would consider to be "purely algebraic":  $$0 \leq (a - b)^2 = a^2 + b^2 - 2ab,$$ so $$ab \leq \frac{a^2}{2} + \frac{b^2}{2}.$$ What is the term for a sentence which reads same forwards and backwards? Please note, I'm not asking for a palindrome.  I mean to say that only the word  order is rearranged, not the actual spelling of the word.  An example might be as follows:     First ladies rule the State and state the rule: ladies first. How do I split a string, breaking at a particular character? I have this string  'john smith~123 Street~Apt 4~New York~NY~12345'   Using JavaScript, what is the fastest way to parse this into  var name = "john smith"; var street= "123 Street"; //etc... How is it like to live in Helsinki?  What is it like to live in Helsinki?  How is living in Helsinki?  What are the differences between these three sentences and what is the common way to ask someone for their opinion about the city they live in? Divergent infinite series $n!e^n/n^n$ - simpler proof of divergence? Invisible space when trying to remove file (but exclude all files in a list)? I'm trying to accomplish a simple task using the excellent post : I would like to remove all files from a folder except those listed in a .txt file contained in the folder. The syntax works fine, but for some reason all files are removed - basically the script is saying that there are no correspondences between the filenames in the folder and those in the .txt file - but I can see that there are!   I thought maybe there might be some invisible white space after my file names that I cannot see (in the folder or the .txt file). But I don't think so...Is there another solution that I am not thinking of? Relay: higher voltage allowed at lower current? Is it safe to use a 30VDC/1A relay for a voltage of 60V but a current of &lt;100uA? E.g. this one: Is it possible to use the startup.blend UI layout in older files? Ideals in valuation rings How do I prove the fact that for any valuation ring $V$ the ideals are totally ordered under inclusion? There is a common story that airline ticket prices rise significantly if you buy them less than two weeks before departure.  And that any time before that will yield standard prices.  Is that advice valid for flying during holiday seasons?  As an example: if I want to fly coast to coast USA on December 7th, must I buy my ticket ASAP, or would I get a similar price buying on November 21st? Find generator of multiplicative group of $\mathbb{F}_{27}$ I have a finite field $\mathbb{F}_{27}$. I need to find an element of order 13. I know that multiplicative group of this field is cyclic with order 26. So I want to find a generator $g$ of this cyclic group, then $g^2$ will have order 13. Also I know that all elements of this field can be represented by polynomials from $\mathbb{F}_3[t]$, where t is root of irreducible polynom $x^3-x-1$.  Probably we can find generator of $\mathbb{Z}_{26}$ and than build an isomorphism to $\mathbb{F}_{27}\setminus 0$.  Anyway I don't know were to start.  Thanks! How to update Ubuntu terminal? How to update Ubuntu terminal? I have float raster and now I want to convert it to vector. How is it possible with the Python GDAL library?  I have tried with gdal_polygonize.py of GDAL utilities on the command line and it worked excellently. But this utility is based on GDALPolygonize() of C++ library and I want to C++ method GDALFPolygonize() to be used instead, which manipulates float raster data as far as I know. What is the difference between a PDU and a power strip (both 120V, 15A)? I just chatted with an APC rep about upgrading the UPSes at our office. She recommended a single higher-capacity 6-outlet Smart-UPS to replace the four Back-UPS units we currently have. When I asked how she recommended plugging in all the current devices, she recommended using a APC's  PDU, but said not to use a power strip. At first she said I had to use an APC brand PDU, but after I inquired about using a Tripp-Lite PDU, she said any brand PDU would be fine.  The APC PDU previously referenced looks like a standard 120V power strip with overload protection but no surge protection. Other than overload protection (which seems redundant if plugging into the UPS), is there something else I'm missing, or should any power strip (without surge protection) be fine?  Edit: I didn't mention it earlier, but we don't have a proper rack--though I did still plan to mount the PDU or power strip to something. I guess I'm wondering if there's any special reason I should pay as much as $180 for the low-end APC PDU (which just looks like a power strip to me) vs. $20-$30 for a . Are the contents of a loot box determined at the time it is awarded or when it is opened?  For example, if you collect multiple loot boxes before a special event but opened them during the special event, would they have the potential of spawning rewards from that event? STI vs STD vs Sexually Transmitted Virus sum of noncentral Chi-square random variables I need to find the distribution of the random variable  $$Y=\sum_{i=1}^{n}(X_i)^2$$ where $X_i\sim{\cal{N}}(\mu_i,\sigma^2_i)$ and all $X_i$s are independent. I know that it is possible to first find the product of all moment generating functions for $X_i$s, and then transform back to obtain $Y$'s distribution. However, I wonder whether there is a general form for $Y$ like the Gaussian case: we know the sum of independent Gaussian is still a Gaussian, and thus we only need to know the summed mean and summed variance.   How about all $\sigma^2_i=\sigma^2$? Will this condition make a general solution? I need to build a list of files present in a directory but also pass in a file containing a list of directories to exclude.  I've seen the below suggestion but I've had no luck with it when it comes to the type flag:  find $dir_name $(printf "! -name %s " $(cat $exclude_file))   Is there a way I can do it or will I need to create the entire list and then work through it removing ones that partially match ones in the exclude directory. Windows 10 ver 1607: File Explorer long paths not working? I updated to the Windows 10 home anniversary edition version 1607 and set LongPathsEnabled to 1 with regedit.exe but the File Explorer doesn't seem to work with long paths still. If you select a long path file and try to rename it, no option will be available. I restarted the computer after making the changes and update.   Is there any way to enable renaming in the File Explorer in the new updated version? Did I miss a step somewhere?