Can 's be used as a contraction of was?  For example, can "maybe she's born that way" mean "maybe she was born that way"?
Is there a contraction for "I was"?    There are contractions for "I am" (I'm), "I will" (I'll), "I have" (I've), "I would" (I'd), and yet the simple past tense seems conspicuously missing. Why is that? Does that reasoning apply to "I did" and "I had" as well?
Types of photon qubit encoding How many types of qubit encoding on photons exist nowadays? I know only two:   Encoding on polarization: $$ \lvert \Psi \rangle = \alpha \lvert H \rangle + \beta \lvert V \rangle $$ $$ \lvert H \rangle = \int_{-\infty}^{\infty} d\mathbf{k}\ f(\mathbf{k}) e^{-iw_k t} \hat{a}^\dagger_{H}(\mathbf{k}) \lvert 0 \rangle_\text{Vacuum} $$ $$ \lvert V \rangle = \int_{-\infty}^{\infty} d\mathbf{k}\ f(\mathbf{k}) e^{-iw_k t} \hat{a}^\dagger_{V}(\mathbf{k}) \lvert 0 \rangle_\text{Vacuum} $$ Time-bin: $$ \lvert \Psi \rangle = \alpha \lvert 0 \rangle + \beta \lvert 1 \rangle $$ $$ \lvert 0 \rangle = \int_{-\infty}^{\infty} dz\ f\left(\frac{t -z/c}{\delta t_{ph}}\right) e^{-i w_0 (t-z/c)} \hat{a}^\dagger(z) \lvert 0 \rangle_\text{Vacuum} $$ $$ \lvert 1 \rangle = \int_{-\infty}^{\infty} dz\ f\left(\frac{t -z/c+\tau}{\delta t_{ph}}\right) e^{-i w_0 (t-z/c+\tau)} \hat{a}^\dagger(z) \lvert 0 \rangle_\text{Vacuum} $$   Is there anything else? Where to find Birth and Death Records for Bucharest, Romania? My husband's family came from Bucharest. Specifically his mother was born in Sibiu.  I have been able to piece together names and relations of several grand and great grandparents from word of mouth and some fortunate pictures they had of the cemetery in Sibiu.  I cannot however find any records of birth's and death's for any of them.   Are there sites or organizations that hold records for Romania? I've created a new user by using "User Accounts" in "System Settings". How do I grant rights so that this new user can have the same level of access as root? Selecting one every n frames from a video using ffmpeg I want to know the memory usage of my Python application and specifically want to know what code blocks/portions or objects are consuming most memory. Google search shows a commercial one is  (Windows only).  And open source ones are  and .  I haven't tried anyone, so I wanted to know which one is the best considering:   Gives most details. I have to do least or no changes to my code. diameter on a compact metric space I have troubles showing the following:  Let $(X,\rho)$ be a compact metric space and $F \subset X$ a closed subset. Prove that if diam $F &lt; \infty$, then there exist $x_{0}, y_{0} \in F$ such that diam $F= \rho(x_{0},y_{0})$.  It looks so trivial yet hard to find the trick. I installed Ubuntu (twice actually) onto the same drive. I wanted to 'try again' since one of them didn't install correctly and the other installed differently, but it worked.   I was getting frustrated with the GRUB menu because it was really sloppy (There were two Windows options - one with the Windows bootloader to go into Ubuntu, and two different versions of Ubuntu from the first install for some reason and memtest, etc.).  In my attempts at getting rid Ubuntu to do a fresh installation, I went ahead and deleted the partitions that weren't swap or main via Windows 7. As I said, I am a noob.  Now, even though I though I completely got rid of Ubuntu, including the GRUB menu, when I boot my PC I am brought directly to GRUB Rescue. And from what I've found from other forums, GRUB rescue isn't even completely functional for me (it doesn't recognize any commands that it should support besides ls. It also returns unknown filesystem for any partition I try to view or boot.)  Is there any way that I can boot straight into Windows? I fear I may have gone about deleting those partitions in the wrong way. If so, what are my options? Calculating determinant with different numbers on diagonal and x everywhere else I'm having troubles solving the following determinant:  $$\left|   \begin{array}{cccc}     a_1 &amp; x &amp; \ldots &amp; x \\    x &amp; a_2 &amp; \ldots &amp; \vdots \\     \vdots &amp; \ldots &amp; \ddots &amp; x \\     x &amp; \ldots &amp; x &amp; a_n \\   \end{array} \right|$$  I have tried coming up with recurrent formula, but there's always one lingering row and column. I also tried finding values of x for which determinant is 0, hoping I could get a nice polynomial solution, with no luck.  By subtracting first row from every other I get somewhat nicer result, but there's still that one row/column which I can't solve. If all other columns are added to the first one and then I subtract the first row, then the column doesn't depend on x anymore, but I haven't found 1..n much more useful. Is it possible for information to be transmitted faster than light by using a rigid pole? Is it possible for information (like 1 and 0s) to be transmitted faster than light?   For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.   The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.  Would this actually work? A doubt on the definition of limit of a function definition I want to prove the definition of limit of a function from definition (1) to definition (2).  (1) A function $f(x)$ is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for every sequence $\{x_n\}$ with limit $x^*$, the limit $\lim_{n-&gt;\infty}f(x_n)$ exists and is equal to $f^*$. (2) A function is said to have $f^*$ as the limit as $x$ tends $x^*$ iff for each $\epsilon &gt;0$, there exists a $\delta_\epsilon &gt;0$ such that $|f(x)-f^*| &lt;\epsilon \forall |x^*-x|&lt;\delta_\epsilon$  I am confused about the steps. Suppose I am given an $\epsilon &gt; 0$ and $x^*$. I have to show the existence of a $\delta_\epsilon &gt;0$ such that for all $x$ satisfying  $|x^*-x|&lt;\delta_\epsilon$ I can construct a sequence $x_n$ which converges to $x^*$ and $x_n=x$ for some $n \geq N$. Then I can say that $f(x_n)-f^*=f(x)-f^* &lt; \epsilon$. I think I may have made some mistake about the steps.  My main confusion is the following : Suppose I choose $\delta_\epsilon=\epsilon$. Then if a sequence $\{x_n\}$ converges to $x^*$ then $x_n=x$ (where $x$ satisfies $|x-x^*|&lt;\epsilon$) for some $n\geq N$. Now, $\lim_{n-&gt;\infty}f(x_n)$ exists implies there exists an $M$ such that $\forall n\geq M$, $f(x_n)-f^* &lt;\epsilon$. Now, I need to show that for some $n \geq M$ indeed $x_n=x$. How do I show that ? This $M$ and $N$ are different. Einstein-Hilbert action as an effective field theory I have read the following statement:      "The Einstein-Hilbert action can be seen as an effective field theory: setting $g_{\mu\nu}= \eta_{\mu\nu}+h_{\mu\nu}$, one gets a free Lagrangian for the field $h_{\mu\nu}$ plus interactions."   Now, how is it possible to define all the interaction terms?  EDIT: I ask apologize if my statement was appeared unclear: I have created a  which is more precise; please don't continue to consider seriously this one. How to put a full stop at the bottom, not mid-line, after an aligned matrix? Is it possible to prove that $1+1 = 2$? Or rather, how would one prove this algebraically or mathematically? To tell about a guess about a case in the past, why use "would+have+past participle" instead of "must+have+past participle? I have seen this sentence in an article on bbc, which is about how people lived thousands of years ago. &quot;When this Neolithic home was built, it would have had a cosy roof of turf..&quot; When I read it, I got confused. Because the fact seems as a simple past situation or guessing/assumption about something in the past. it simply gives information about a past event, eg &quot;when I was a child, I had a blue toy car. I have been making a lot of research on whether or not this structure &quot;would+have+past participle&quot; could be used instead of the simple past or &quot;must+have+past participle&quot;, but I could not find any satisfying explanation. Almost all grammer contents cover this structure is used when we imagine the opposite of what actually happened in the past eg. &quot;referring to a missed opportunity&quot; (eg. &quot;if you had come to the party, you would have seen Tom.&quot;), But, in this case of this sentence, &quot;type 3 conditional&quot; is irrelevant. It is not an if sentence,  It simply gives information about how this house was like or was probably like when it was built long ago. Just like it would be If and old lady would want to tell about &quot;how she was like when she was a child years ago. she would simply say &quot;when I was a child, I had long curly hair.**. So &quot;when I was a child, I would have had long curly hair.&quot; would be wrong. So, my question is: 1-Does this structure &quot;would+have+past participle&quot; completely replace simple past sentences? or can be it be used instead of simple past? 2- If this structure was simply used because the author was not %100 sure about the fact as it was a long long time ago -so he wanted to make a guess or assumption, why did he not simply use &quot;must+have+past participle&quot; or &quot;it was likely that blah blah&quot; which must be used for guessing or assumptions about past happenings. Would it not have made more sense if it was like: &quot;When this Neolithic home was built, it must have had a cosy roof of turf. How to avoid being prompted for a password by sudo? I know I can become root (super user) via the su command but I have to authorize it after entering the commands. Is there a way I can become root and authorize (with password) in one line I have to give a combinatorial proof of  $$\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}.$$  I find it difficult to solve such problems. I'm not a brilliant person and never will be so I need to have algorithms to solve most problems. Usually I won't just "see" solutions unless I have a thorough enough understanding of a theory. This is also the case here. I know what the symbols mean, but I don't see what I should count and how to obtain the identity.  I think the right-hand side counts $n$-element subsets of a $(2n-1)$-element set with one element chosen to be "special". I think I should find a partition of the set of such subsets into $n$ parts so that the left-hand side is the sum of the cardinalities of the parts. Is there $n$ of anything on the right-hand side? Well, there are $n$ choices for the "special" elements, but only after I've chosen the $n$-element subset. Otherwise I can choose the "special element" in $2n-1$ ways.  This is a homework problem so I probably shouldn't ask for a full solution. But I would like to have some guidelines for approaching such problems, perhaps based on this example. How can I include custom post types on a tag page? I'm using custom post types, but they don't appear on tag pages along with regular posts and i'd like to include both standard and custom post types on tag or category pages. What would be required before the loop to include all posts? (including custom type). Updated: To add, I found this code , which worked perfectly for the first part: add_filter('pre_get_posts', 'query_post_type'); function query_post_type($query) {   if ( is_category() || is_tag() &amp;&amp; empty( $query-&gt;query_vars['suppress_filters'] ) ) {     $post_type = get_query_var('post_type');     if($post_type)         $post_type = $post_type;     else         $post_type = array('post','cpt'); // replace cpt to your custom post type     $query-&gt;set('post_type',$post_type);     return $query;     } }  Second question still remains though: Is there a way to allow readers to filter by post type? So either of the following would work..  example.com/tag/blue?post_type=custom example.com/tag/blue?post_type=post Random string that matches a regexp As a 8th grader I am still a newbie at science and I have problems understanding the forces that I can not imagine and one of these "forces" is the moment.  We are told that,  $$\text{moment}= Nm$$ but how can a certain force (i.e. $N$) be applied when there is $m$? How does it depend on the length of the considered object?  And how can 1 moment be defined on the basis of that representation?  And what would be the effect if the moment value is increased by the newton part as opposed to the effect when the value is increased by the length part.  Or is the result the same in both cases? I am a computer scientist, and one of my professors today used the symbol $\propto$. I tried to search that using google, but it returns no results, and I do not even know its name.  So, I would like to ask, what does the operator $\propto$ mean? What is its name, and how is it used?