Story With Character Named Briar
Young Adult Fantasy about children living with an elderly woman and learning magic related to their skills
Combinatorics - binary - very interesting question I tried to solve this problem without any success. I really hope that you will know the answer. $f(n,m)$ presents the number of binary strings (empty string included) that include at most n times '1', and at most m times '0'.      Prove: $$f(n,m) = \binom{n+m+2}{n+1}-1$$ proper usage of didn't had or didnt have What is the "N+1 selects problem" in ORM (Object-Relational Mapping)? The "N+1 selects problem" is generally stated as a problem in Object-Relational mapping (ORM) discussions, and I understand that it has something to do with having to make a lot of database queries for something that seems simple in the object world.  Does anybody have a more detailed explanation of the problem? Let $X$ de a vector space and $A\subset X$. If we define $A+B :=\{a+b|a\in A, b\in B\}$ I am trying to show that    $$ \begin{equation} 2A \subsetneq A+A, \end{equation} $$  i.e., it might happen that $2A \neq A+A$. I was able to show that $2A \subset A+A$, but I am not able to come up with a counterexample to show that the converse is not necessarily true. If I assume $A+A\subset 2A$ and let $x\in(A+A)$, then by its definition we have $x=a_1 + a_2$ for some $a_1,a_2\in A$ I guess I could naively say that $a_1+a_2 = 2(a'_1+a'_2)$ where $a_i=a_i/2$ for $i=1,2$ and I guess $(a'_1+a'_2)$ might not be an element of $A$ in some concrete case but I am not able to come up with anything and I've spent more time than I would like to admit. Any suggestions?  Thank you. My 13 year old daughter says she wants to be a boy. This is out of character for her. Is this a phase? My daughter, 13, has said she wants to be a boy. A little background: we moved to a new state a year and a half ago. In her new school, she felt isolated among her peers until she met a girl in art, and became good friends. She joined the drama club, and made  friends with some 8th graders. They joined “the diversity club”. This club is a LGBT club. The kids put on a play they wrote and starred in, which had homosexual connotations. “Romeo and Juliet”, but script  rewritten to include  2 females as the couple, for instance.   My daughter got so wrapped up in it, that her life was as if she was copying the play. She’s no longer friends with the friend from art, but remains close with the 8th grade crowd. They all labeled themselves. One week, my daughter said she was gay, then, changed to bi, then onto pan. (I had to google that one). Now she is emphatic about being disgusted with her body and wants to be a boy. She wants to donate all the “girly” clothes she picked out last year, and tossed out all the makeup she bought a few months ago.   All her life, she was the classic girly girl. She had crushes on boys, and she and this boy were inseparable since first grade. She was sad when it came time to move away. When we settled here, she became sullen and angry, putting herself down. She now sees a therapist who she really likes. We’ve been working on her self esteem issues. She’s wanting us to call her “he” and by a male name. I can’t do that. She’s my daughter. She is female. Had we seen this coming, maybe I could come to accepting. But it happened out of the blue.  Sometimes the old her comes back-I got a makeup sample and she was interested in trying it, looked at me, then quickly put it down and said “ewww, makeup”—just a few months ago, she bought a bunch. She’s now wanting to wear boys clothes and talks of wearing a suit to her prom. She is very impressionable, and seems affected by viral YouTube videos about kids coming coming out to their mothers, and the mothers gleefully embrace with happy tears. She has told me when she’s 18, she’s having her breasts removed.    Nothing seems normal to me anymore-in terms of how she always was-this new situation just doesn’t fit.  My gut tells me this is a phase.  I’m hoping it’s a phase. But with all I’m seeing in the media about this, I’m not sure. I love her; this is too much for me to process. I’m a stay at home mom; we were inseparable. I knew her. Until now.:(  She cut off all her beautiful hair, and wears boys shorts, baggy tee shirts, and bought this awful men’s deodorant spray. Please help me sort this out. I’m at my wits end.  Do you think this is a phase? Is this common? What is wrong with defining \bal as \begin{align}? Accidentally moved directories under root Equation mode, labelling equations I have the following   \[K^{-1}\left\|\sum\limits_{n=1}^N a_ny_n\right\|    \leq \left\|\sum\limits_{n=1}^N a_nx_n\right\|    \leq K\left\|\sum\limits_{n=1}^N a_ny_n\right\| (\dagger)\]   But the dagger doesn't appear at the right hand end of the page. How can I Get it so that it does appear on the end of the page? the \hfill command doesn't seem to work. Thank you. A complete ring with respect to an ideal I would like to know what does it mean to say " a ring $R$ is complete with respect to some ideal $I \subset R$.  Is it like, we define a metric by saying two elements in $R$ is "close" if the difference lies in a higher power of $I^n$ and $R$ is a complete metric space? I want to change my computer's password. Right now my password is abc123. I run this command:  sudo passwd   I entered my current password and then a new one but the change does not take effect. How can I resolve this problem ? Solve $y’ = \frac{2-xy^3}{3x^2y^2}$ using Bernoulli form Solve, by bringing the equation to Bernoulli form: $$ y’ = \frac{2-xy^3}{3x^2y^2} $$  Therefore we want to bring it to a form like: $$ y’ + p(x)y = q(x)y^n $$ So working with the equation i get: $$ y’ - \frac{2}{3x^2y^2} = -\frac{xy^3}{3x^2y^2} = -\frac{y}{3x} $$ I don’t see how to get to Bernoulli equation from here... While studying I read about the principle of underdetermination of scientific theories. I made some researches online but I am more confused than before. I read about the Quine-Duhem holistic thesis, but I do not know if is the same as underdetermination. I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a proposed solution. Any input from you guys would be welcome, as to what is the best way to go about this.  Problem:  There was a jail with 100 cells in it, all in a long row. The warden was feeling very jolly one night and told his assistant that he wanted to give all the prisoners a wonderful surprise. While they were sleeping, he wanted the assistant to unlock all the cells. This should be done, he told the assistant, by putting the key in each lock, turning it once. The assistant did this, then came back to report that the job was done. Meanwhile, however, the warden has second thoughts. "Maybe I shouldn't let all the prisoners free," he said. "Go back and leave the first cell open, but lock the second one (by putting the key in and turning it once). Then leave the third open, but lock the fourth, and continue in this way for the entire row." The assistant wasn't very surprised at this request as the warden often changed his mind. After finishing this task, the assistant returned, and again the warden had other thoughts. "Here's what I really want you to do," he said. "Go back down the row. Leave the first two cells as they are, and put your key in the third cell and turn it once. Then leave the fourth and fifth cells and turn the key in the sixth. Continue down the row this way." The assistant again did as instructed. Fortunately, the prisoners were still asleep. As a matter of fact, the assistant was getting pretty sleepy, but there was no chance for rest yet. The warden changed his mind again, and the assistant had to go back again and turn the lock in the fourth cell and in every fourth cell down the row. This continued all through the night, next turning the lock in every fifth cell, and then in every sixth, and on and on, until on the last trip, the assistant just had to turn the key in the hundredth cell. When the prisoners finally woke up, which ones could walk out of their cells?  Proposed solution:  Ten cells are left open after this process. Every cell that is a perfect square will remain open (1, 4, 9, 16, 25, 36, 49, 64, 81, and 100). If a number is not a perfect square, then it has an even number of divisors, therefore it will be "toggled" an even number of times and end up where it started (closed). Perfect squares have an odd number of divisors, so they will end up the opposite of where they started (open). How to use siunitx and tabularx together? I'm using the tabular features of siunitx (for what it is worth: v1.3 since I'm on TexLive 2009) to align numbers in tables, eg.  \begin{tabular}{ p{1.5cm} S S S } bla &amp; 1.23 &amp; 4.5 &amp; 67.89 \tabularnewline \end{tabular}   and that works perfectly fine.  Now I would like to have this table span a specific width, or rather to have several tables to have the same width. For this I would normally use tabularx  \begin{tabularx}{\textwidth}{ p{1.5cm} X X X } bla &amp; 1.23 &amp; 4.5 &amp; 67.89 \tabularnewline \end{tabular}   Now, is there a way to combine the two? To have the number formatting and alignment features of siunitx inside an automatically resizing table? What are XML namespaces for? This is something that I always find a bit hard to explain to others:  Why do XML namespaces exist?  When should we use them and when should we not? What are the common pitfalls when working with namespaces in XML?   Also, how do they relate to XML schemas? Should XSD schemas always be associated with a namespace? Find the exact value of the infinite sum $\sum_{n=1}^\infty \big\{\mathrm{e}-\big(1+\frac1n\big)^{n}\big\}$ How can we find the exact value of the infinite sum  $$ \displaystyle\sum_{n=1}^\infty \left\{\mathrm{e}-\Big(1+\frac1n\Big)^n\right\}? $$  This problem appears in:  , p.114. How to get Url Hash (#) from server side 3 Statements of axiom of choice are equivalent This winter I started to study much harder the set theory and especially the axiom of choice. Unfortunately, I have problems with solving the next exercise:  Prove that the 3 statements of the axiom of choice are equivalent :  1) For any non-empty collection $X$ of pairwise disjoint non-empty sets, there exists a choice set.  2) For any non-empty collection $X$ there is a choice function.  3) For any non-empty set $X$, there exists a function $f:P(X)\setminus\{\varnothing\}\to X$ so that for any non-empty set $A\subseteq X$, $f(A) \in A$. Make Excel open some hyperlinks with non-default browser A bunch of our network/server/storage hardware uses web interfaces for their administrative portals. I'm currently using an Excel 2010 worksheet to keep track of each device. I have one column set aside to list the URL for each web interface. This makes it easy to simply click the URL to open each administrative portal.  My default browser is Firefox. However, some of the administrative portals don't play well with Firefox and require the use of IE. Until now, when I want to open a hyperlink in IE, I have to manually open IE, copy the URL from the Excel worksheet, and paste it into the IE address bar (otherwise it will open in Firefox if I simply click it). It's just an annoying extra couple of steps.  So without changing Firefox as my default browser, is there a simple way in Excel 2010 to tell it which hyperlinks to open in IE when they are clicked? I want to choose specifically which links open in which browser  (For reference I'm using Windows 7 Enterprise 64-bit) Abiword starts automatically each restart Abiword starts automatically each restart, on any user. Already checked out Startup Applications. Remember session is turned off.   ()  Additional info, may be it'll give a clue - I configured VNC server on this machine to run, so sometimes, in additional to regular Ubuntu/Unity sessions I start XFCE4 session. I think this behavior started after VNC4 configuration, but ~/.vnc/xstartup does not contain abiword - just regular xfce startup stuff.  What are additional places where I can look?