The whole problem is: Find a function that is in Bounded variation(BV) but not in Absolutely Continuous(AC). It's not too hard to find a function is in BV, but how do we prove a function is not AC?
I know that a continuous function which is a BV may not be absolutely continuous.  Is there an example of such a function?   I was looking for a BV whose derivative is not Lebesgue integrable but I couldn't find one.
How does Linux kernel compare to microkernel architectures? I read once that one advantage of a microkernel architecture is that you can stop/start essential services like networking and filesystems, without needing to restart the whole system. But considering that Linux kernel nowadays (was it always the case?) offers the option to use modules to achieve the same effect, what are the (remaining) advantages of a microkernel? The (countably infinite) wedge sum of circles is quotient of  disjoint countable union of circles $\amalg S_i$, with points $x_i\in S_i$ identified to a single point, while the infinite earring H is the topological space defined by the union of circles in the Euclidean plane $\mathbb{R}^2$ with center $(1/n, 0)$ and radius $1/n$ for $n = 1, 2, 3, ...$. In the definition of countably infinite wedge sum of circles, it is not specified the size of circles, the points which to be identified to a single point etc. So we can take disjoint union of circles of radius $1/n$ and identify a point from each to a common single point to get the infinite earring. I couldn't understood the difference between these two topological spaces. Can one explain more precisely the difference between these two spaces? Does a magic item used as an improvised weapon count as a magic weapon? Layers with same coordinates not lining up 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. Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$ what does the ldapadd error: "additional info: objectClass: value #2invalid per syntax mean? Does anyone know of a script that can select all text references to URLs and automatically replace them with anchor tags pointing to those locations?  For example:  http://www.google.com   would automatically turn into  &lt;a href="http://www.google.com"&gt;http://www.google.com&lt;/a&gt;   Note: I am wanting this because I don't want to go through all my content and wrap them with anchor tags. Fluent and Query Expression — Is there any benefit(s) of one over other? Not able to calculate sum of multiple column where file data in different format .csv I have a scenario where i want to calculate sum of column   SAL|CAL|TAG|VAL 12.11"|"1.1"|"2.1"|"1.1 13.11"|"1.1"|"2.2"|"2.2 14.11"|"1.1"|"2.4"|"2.4   My below code not giving output giving output as 0.00  I need output for this column CAL VAL  awk -F'|' '{T+=$2} END { printf "%.2f\n", T }' demo.txt   output :  6.7 5.7 Automating the appearance of email addresses as images Publishing pdf manuscripts on the web with emails embedded in the file results in spam.  More generally, I am looking for a way to automate the conversion of a string to an image.  It's quite easy to solve this old problem using  (more ). The trouble is that you need a distinct file and typesetting run, and you end up with unnecessary image files that you cannot delete carelessly lest you also delete non-generated images.  Can you think of a way to do this on the fly? It's understood that people will have to type the email addresses if they need to message you, but that's the point.  More briefly/concretely...  With what can one replace #1  \documentclass{article} \newcommand\showasimage[1]{#1} \begin{document} \showasimage{joe@foo.bar} \end{document}   such that #1 appears as an image?  Edit  It would be really nice if the pdf file remains vectorial. What is the opposite of "personification"? I want a word that means the opposite of personification.  What is the correct word for describing people with the characteristics of an object/as if they are objects?  I found the word chremamorphism on some forums, but it doesn't seem to be included in the two online dictionaries I searched. Let $A ∈ M_{m\times n}(\mathbb{Q})$ and $B ∈ \mathbb{Q}^m$. Suppose that the system of linear equations $AX = B$ has a solution in $\mathbb{R}^n$. Does it necessarily have a solution in $\mathbb{Q}^n$?  Where do I start?    I feel I can use this to :  $$x_i=\frac{1}{a'_{ii}}\left(b'_i - \sum_{j=i+1}^{k} a'_{ij} x_j \right).$$    Here is a thought that just crossed my mind, but I'm not sure if this is legal:  Suppose $Y\in \{\mathbb{R}\setminus \mathbb{Q}\}^n$ and $Y'\in\mathbb{Q}^n$ are solutions to $AX=B$. Then $AY=AY'=B$, or $A(Y-Y')=A(Y+(-Y'))=0$, but  addition between $\{\mathbb{R}\setminus \mathbb{Q}\}^n$ and $\mathbb{Q}^n$ is . . . Quoted headings are rendered properly on preview but not when posted With markdown, you can use some dashes for headings. For example, this: Hello ---- this is some other text  renders as this: Hello this is some other text This is fine and works well. When I want to quote that text is when the problem arises, since this Markdown: &gt; Hello &gt; ---- &gt; this is some other text  When written down shows well in the preview but not when posted:  Hello this is some other text   As an example, see an screenshot of the preview:    and a screenshot of the posted content, where the ---- becomes a &lt;hr&gt;:  Note a similar bug I also reported: . How to extract code of .apk file which is not working? Batch Processing Quick Query I have like 50000 records that meet my condition for batch processing. My batch process begins at say 10:01 AM and ends at 10:10 AM. I set my batch size to be 200.  Can someone tell me what would happen  a) If an user creates a record at 10:03 AM that meet my condition...will this record be also be processed or not ?  b) Will the records which are getting processed during Batch 1 are technically locked till that particular batch is processed completely ?  c) What will be the behaviour if a record in Batch N does not meet my condition anymore but that particular batch has already been started to process ?  d) Is it possible to create a parallel processing of sorts such that Salesforce (instead of running one batch at a time) it will start processing parallely with multiple batches ?  I searched online and I could find manual/instructions with respect to how to run batch apex but I am not able to get clarity with respect to these specific cases. Why is it called John Dies at the End? The 2012 adaptation of David Wong's "John Dies at the End" ends without John dying at the end at all. While the core of the film espouses the belief that time is not linear, the word "end" suggests there is a beginning and an end to things.  Why is the movie called John Dies at the End? 80s-90s anime (movie or series) in which an armored girl exchanges age with a dying man on a beach Why do light disappears the moment we switch off the source (inside the wooden box)? For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks. Watts P.M.P.O. and audio equipment power I am a beginner in electrical engineering, and to begin learning I decided to look into audio amplifiers. I have seen that the power of audio amplifiers is often described in the units of watts, watts RMS, and watts PMPO. So far, the only one of those units that I think I understand is watts. For instance, I just recently made . If I think: &quot;What is the power of my amplifier supposed to be?&quot;, then my thought process goes like this:  The transistors I used are the TIP120, which have a maximum rated power of 65W. Then, I decide that 60W is a safer maximum which would be reached if my amplifier runs 19V through one of my 6Ω speakers. Therefore, the power of my amplifier is 2x60W.  Then, I look at the datasheets of audio amplifier ICs, like the TPA3116 that says: &quot;50W into a 4Ω load at 21V&quot;, which makes me conclude that in that setting it'll output 14V maximum into the speaker, which I think makes sense. But then, I look at the datasheet of the TDA7294, and they talk about &quot;RMS Power&quot; and &quot;RMS Music Power&quot;, units which I couldn't find clear information about. Then, I look at home audio systems, like a Panasonic Stereo System I have which has &quot;9500 Watts P.M.P.O.&quot; written on the front. 9500W? That sounds stupidly high to me, but then I look again and it has 300W written on the back of it. If I'm correct, maybe a 1kW home stereo system could make sense, but a 2kW or greater one would not exist. So... Are my conclusions about  and the TPA3116 correct? Are my conclusions about audio equipment power correct? Are WattsPMPO, WattsRMS and RMSmusicpower, real useful units?