I've been an English student since school, however, I always feel like I'm mispronouncing the word &quot;the&quot;. Oxford online dictionary defines the pronunciation of 'the' as: /ðə/, /ðiː/, /ðɪ/. So, are the three correct in every situation?, if not, when should I use each of them?
The is sometimes pronounced &quot;tha&quot; (/ðə/) or &quot;thi&quot; (/ðiː/). Which is the correct pronunciation of this word? Are both correct and used interchangeably at specific places? If the second question is correct, please provide the rule of pronouncing at different places.
Get exit status of process that's piped to another I have two processes foo and bar, connected with a pipe:  $ foo | bar   bar always exits 0; I'm interested in the exit code of foo. Is there any way to get at it? Equivalence of definitions of prime ideal in commutative ring I want to extract infromation from logs using a shell script for a particular time range . A line in logs looks like this:  [14:58:27:176][15-10-2015]: testing1-vidya-Thu Oct 15 11:49:27 IST 2015 [14:59:27:178][15-10-2015]: testing2-vidya-Thu Oct 15 11:49:27 IST 2015 [15:00:27:179][15-10-2015]: testing3-vidya-Thu Oct 15 11:49:27 IST 2015 [15:01:27:180][15-10-2015]: testing4-vidya-Thu Oct 15 11:49:27 IST 2015 [15:01:27:181][15-10-2015]: testing5-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:182][15-10-2015]: testing6-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:183][15-10-2015]: testing7-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:184][15-10-2015]: testing8-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:191][15-10-2015]: testing9-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:192][15-10-2015]: testing10-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:193][15-10-2015]: testing11-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:208][15-10-2015]: testing12-vidya-Thu Oct 15 11:49:27 IST 2015 [15:04:27:209][15-10-2015]: testing13-vidya-Thu Oct 15 11:49:27 IST 2015 [15:49:27:210][15-10-2015]: testing14-vidya-Thu Oct 15 11:49:27 IST 2015 [13:02:17:209][15-10-2015]: testing13-vidya-Thu Oct 15 11:49:27 IST 2015 [15:04:27:209][16-10-2015]: testing13-vidya-Fri Oct 16 11:49:27 IST 2015 [15:49:27:210][16-10-2015]: testing14-vidya-Fri Oct 16 11:49:27 IST 2015   I need to extract data in specific intervals. for example in between 14:59 to 15:03 on 15-10-2015 as shown below:   [14:59:27:178][15-10-2015]: testing2-vidya-Thu Oct 15 11:49:27 IST 2015 [15:00:27:179][15-10-2015]: testing3-vidya-Thu Oct 15 11:49:27 IST 2015 [15:01:27:180][15-10-2015]: testing4-vidya-Thu Oct 15 11:49:27 IST 2015 [15:01:27:181][15-10-2015]: testing5-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:182][15-10-2015]: testing6-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:183][15-10-2015]: testing7-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:184][15-10-2015]: testing8-vidya-Thu Oct 15 11:49:27 IST 2015 [15:02:27:191][15-10-2015]: testing9-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:192][15-10-2015]: testing10-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:193][15-10-2015]: testing11-vidya-Thu Oct 15 11:49:27 IST 2015 [15:03:27:208][15-10-2015]: testing12-vidya-Thu Oct 15 11:49:27 IST 2015   I am new to shell script.I have tried with grep command . 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The example I had in mind was the 2-dimensional extension $\mathbb{R} \subset \mathbb{C}$ with $\mathbb{C}$ being isomorphic to $\{ \begin{pmatrix}a&amp;-b\\b&amp;a\end{pmatrix} : a, b \in \mathbb{R}\}$. Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$ Let $x \in \mathbb R$  Find a closed form of $\int_0^\infty\dfrac{\cos(xt)}{1+t^2}dt$ .   Let me give some context: this is an exercise from an improper integrals course for undergraduates. My teacher was not able to give a valid solution without  resorting to Fourier series.   He actually wanted to prove first that the function is a solution of the ODE $$ y-y'' =0$$ without succeeding in proving it.   Anyway the result sould be $\dfrac{\pi}{2}e^{-x}$  Thanks for any help on this subject. I've found a nasty VBS way to do this, but I'm looking for a native PoSh procedure to edit the properties of a .LNK file.  The goal is to reach out to remote machines, duplicate an existing shortcut with most of the correct properties, and edit a couple of them.  If it would just be easier to write a new shortcut file, that would work too. What makes a chewy brownie? I've tried many different brownie recipes and most of mine bake to a cake-like consistency. The brownie holy grail for me is crusty top chewy brownies. What can I add/remove/do that will make my brownies chewier? Study the convergence of the following series: $$\sum_{n=2}^\infty \frac{1}{n^\alpha \cdot\ln^\beta(n)} \text{ where }\alpha,\beta \geq 0 $$   Applying d'Alembert criterion I have that $$ \lim_{n\to\infty} \frac{n^\alpha  \ln^\beta(n)}{(n+1)^\alpha  \ln^\beta (n+1)} = \lim_{n\to\infty} \left(\frac{n}{n+1}\right)^\alpha\left(\frac{\ln(n)}{\ln (n+1)}\right)^\beta = 1$$ so the nature of the series is inconclusive.  If $\alpha = \beta = 0$, then the series diverges, since $\sum_{n=2}^\infty 1 = \infty$.  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