I would like to start a new line directly below a certain word in previous line. For example, let the first line begins by 'Let A denote ...' and I want to have 'B denote ...' for the second line. However I want 'B' to be exactly below 'A'. Is there a technical method of doing this in Latex? If you have any other suggestions, please let me know.
I want to typeset a piece of code containing line breaks.  New lines should indent to a specified point in the previous line.  Here is a monospaced example to illustrate what I mean.  Notice how 'case' and 'of' line up below, as well as 'let' and 'in':  swap : forall a, b. Tuple a b -&gt; Tuple b a swap a b x = case x              of tuple a b y z. let x' = tuple b a z y                                in x'   The code I want to typeset is not monospaced, so I can't just use a verbatim environment to get what I want.  The actual LaTeX of the first line, for instance, is  \mathsf{swap} : \forall\alpha,\beta.\;\mathsf{Tuple}\;\alpha\;\beta\to\mathsf{Tuple}\;\beta\;\alpha   How can I align some text to a specific point in the previous line?
Send POST data using XMLHttpRequest Creating a query that uses criteria from two tables? How to convert a number to words in MS Excel Android app? Excel Macros are unsupported in Android and there is also no SpellNum Function in Android . I want a function which can convert a number to words. Is there any way we can achieve this ? eg -  40004  , should be converted to Forty Thousand Four Does a correlation matrix of two variables always have the same eigenvectors? Is there a place where I can look what updates I've installed? What does eno mean in network interface name 'eno16777736' for CentOS 7 or RHEL 7? Under consistent network device naming scheme, what does 'eno' stand for in network interface name eno16777736 for CentOS 7 or RHEL 7? How can I find the files that were stored on my flash drive before I installed Ubuntu to it?   Edit: No, I didn't format it, my files are still on the flash drive root. I just need to know how to access them there. Show that antipodal points remain antipodal under any isometry of $S^2$ "The antipodal map of $S^2$ is the isometry $\bar m$ sending each point $P$ to its opposite point $-P$" (from textbook)  Show that antipodal points remain antipodal under any isometry of $S^2$. In other words, for each isometry f of $S^2$, if $P$ and $P'$ are antipodal, then so are $f(P)$ and $f(P')$  I am unsure how I can define the $P$ and $P'$ so that they are opposites of each other in the antipodal map, and am I supposed to apply the traditional isometries (translation, reflection and rotation) to the points? I don't understand this problem. Brackets in if condition: why am I getting syntax errors without whitespace? I am using the below script to move two days back when script runs at starting two days of the year and also check first and second days of every month and move two days back. if [$month=&quot;01&quot;] &amp;&amp; [$day=&quot;01&quot;]; then         date=&quot;$last_month/$yes_day/$last_year&quot;         fulldate=&quot;$last_month/$yes_day/$last_year&quot; else         if [$month=&quot;01&quot;] &amp;&amp; [$day=&quot;02&quot;]; then                 date=&quot;$last_month/$yes_day/$last_year&quot;                 fulldate=&quot;$last_month/$yes_day/$last_year&quot;         else                 if [ $day = &quot;01&quot; ]; then                         date=&quot;$last_month/$yes_day/$year&quot;                         fulldate=&quot;$year$last_month$yes_day&quot;                 else                         if [ $day = &quot;02&quot; ]; then                                 date=&quot;$last_month/$yes_day/$year&quot;                                 fulldate=&quot;$year$last_month$yes_day&quot;                         else                                 date=&quot;$month/$yes_day/$year&quot;                                 fulldate=&quot;$year$month$yes_day&quot;                         fi                 fi         fi fi  But my bad am getting the below error message Etime_script.sh: line 19: [06=01]: command not found Etime_script.sh: line 24: [06=01]: command not found I'm attempting to build an LED bed lamp that will be powered by 240V mains. The LEDs are  which if I use with a 12V supply and have calculated correctly will draw 0.24W each. I plan to use 5 or 6 of them in the lamp so will consume a maximum of 1.5W.  Initially I thought I'd use a transformer and bridge rectifier to get the required 12V DC but the transformer weighs a ton and is too bulky. The next option was to use a  but I'm wondering is there is a better way?  I think it would be possible to power the LEDs directly from mains using only a rectifier without mains and stepping down the voltage but then it's not safe. Are there any smallish components that can both isolate the mains and supply a DC voltage? "Install Spotify" can't be opened because Apple cannot check it for malicious software I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks. I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? A mathematically mature introduction to Turing Machines and Computability [reference-request] In the computer science course for mathematicians held at my university Turing Machines have been presented very briefly. So much so that I didn't quite get why they are relevant to mathematics. I did understand what a Turing Machine is, but I feel that the presentation given was (for schedule reasons) quite naive and simplified. So I would like to ask if you can point out a good reference for a mathematically mature introduction to turing machines and computability. Is there a more efficient way to clamp real numbers than using if statements or ternary operators? I want to do this both for doubles and for a 32-bit fixpoint implementation (16.16). I'm not asking for code that can handle both cases; they will be handled in separate functions.  Obviously, I can do something like:  double clampedA; double a = calculate(); clampedA = a &gt; MY_MAX ? MY_MAX : a; clampedA = a &lt; MY_MIN ? MY_MIN : a;   or  double a = calculate(); double clampedA = a; if(clampedA &gt; MY_MAX)     clampedA = MY_MAX; else if(clampedA &lt; MY_MIN)     clampedA = MY_MIN;   The fixpoint version would use functions/macros for comparisons.  This is done in a performance-critical part of the code, so I'm looking for an as efficient way to do it as possible (which I suspect would involve bit-manipulation)   EDIT: It has to be standard/portable C, platform-specific functionality is not of any interest here. Also, MY_MIN and MY_MAX are the same type as the value I want clamped (doubles in the examples above). Why is sum of squared residuals non-increasing when adding explanatory variable? In my econometric textbook(Introductory Econometrics) covering OLS, the author write, "SSR must fall when another explanatory variable is added."  Why is it? Background I'm working on a time series data set of energy meter readings. The length of the series varies by meter - for some I have several years, others only a few months, etc. Many display significant seasonality, and often multiple layers - within the day, week, or year. One of the things I've been working on is clustering of these time series. My work is academic for the moment, and while I'm doing other analysis of the data as well, I have a specific goal to carry out some clustering. I did some initial work where I calculated various features (percentage used on weekends vs. weekday, percentage used in different time blocks, etc.). I then moved on to looking at using Dynamic Time Warping (DTW) to obtain the distance between different series, and clustering based on the difference values, and I've found several papers related to this. Question Will the seasonality in a specific series changing cause my clustering to be incorrect? And if so, how do I deal with it? My concern is that the distances obtained by DTW could be misleading in the cases where the pattern in a time series has changed. This could lead to incorrect clustering. In case the above is unclear, consider these examples: Example 1 A meter has low readings from midnight until 8AM, the readings then increase sharply for the next hour and stay high from 9AM until 5PM, then decrease sharply over the next hour and then stay low from 6PM until midnight. The meter continues this pattern consistently every day for several months, but then changes to a pattern where readings simply stay at a consistent level throughout the day. Example 2 A meter shows approximately the same amount of energy being consumed each month. After several years, it changes to a pattern where energy usage is higher during the summer months before returning to the usual amount. Possible Directions  I've wondered whether I can continue to compare whole time series, but split them and consider them as a separate series if the pattern changes considerably. However, to do this I'd need to be able to detect such changes. Also, I just don't know if this is a suitable way or working with the data. I've also considered splitting the data and considering it as many separate time series. For instance, I could consider every day/meter combination as a separate series. However, I'd then need to do similarly if I wanted to consider the weekly/monthly/yearly patterns. I think this would work, but it's potentially quite onerous and I'd hate to go down this path if there's a better way that I'm missing.  Further Notes These are things that have come up in comments, or things I've thought of due to comments, which might be relevant. I'm putting them here so people don't have to read through everything to get relevant information.  I'm working in Python, but have rpy for those places where R is more suitable. I'm not necessarily looking for a Python answer though - if someone has a practical answer of what should be done I'm happy to figure out implementation details myself. I have a lot of working &quot;rough draft&quot; code - I've done some DTW runs, I've done a couple of different types of clustering, etc. I think I largely understand the direction I'm taking, and what I'm really looking for is related to how I process my data before finding distances, running clustering, etc. Given this, I suspect the answer would be the same whether the distances between series are calculated via DTW or a simpler Euclidean Distance (ED). I have found these papers especially informative on time series and DTW and they may be helpful if some background is needed to the topic area: How to change multiple file type associations on the Mac at once? I want to change my default media player in macOS.  (In my case, I want to change it to my own AppleScript-created instance of VLC that I exported as ‘VLC-New-Window.app’, which is scripted to  so that it doesn’t override the existing paused playlist or video file I want to keep in the background.)  It is very tedious to find an example of every file type I use VLC for (whether mkv, avi, mp4, m4v, m4a, m4b, mp3, flac, or m2ts), right-click on it, and manually set the new default program each time.  And honestly I’d like every audio or video file type that VLC can open to be applied here so that I never have to worry about this again.  Is there any method that can help automate this, or do this in batch? How to install Google Chrome How do you install Google Chrome on Ubuntu? 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