When I put ice cubes in a glass of water, I find that sometimes they will stick together and form a sort of "bridge" between them as they melt.  There is usually a visible line where one ends and the other begins, and they break apart if pushed (but for the most part they stick together if they aren't interfered with).  I'm wondering how they form this bridge in the first place if they're melting, and why it stays together.
I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice water mixture comes crashing down. With my open mouth overfilled with ice water, my shirt gets wet – I hate when this happens. After drying myself off, I started thinking why this does happen:   How does ice that starts off loose and separated in water fuse together to form one large clump? What causes the ice-water mixture to stop flowing momentarily and then suddenly starting flowing again? Is it that the ice fuses together in the glass and forms one large clump, and then the friction with the edges builds a "dam-like" situation? Or are there individual pieces of ice fusing with the edges of the drinking glass damming-up the ice?
Is there a geometrical method to prove $x<\frac{\sin x +\tan x}{2}$? Suppose $x \in (0,\frac{\pi}{2})$ and we want to prove $$x&lt;\frac{\sin x +\tan x}{2}$$I tried to prove it by taking $f(x)=\sin x+ \tan x -2x$ and show $f(x) &gt;0 ,when\space  x \in (0,\frac{\pi}{2})$ take f'$$f'=\cos x +1+\tan ^2 x-2\\=\tan^2 x-(1-\cos x)\\=\tan ^2 x-2sin^2(\frac x2)$$ I get stuck here ,because the last line need to be proved $\tan ^2 x&gt;2sin^2(\frac x2) ,when\space  x \in (0,\frac{\pi}{2})$ $\bf{Question}:$ Is there a geometrical method to prove the first inequality ? (or other idea)  Thanks in advance.    $\bf{Remark}: $I can see the function is increasing $when\space  x \in (0,\frac{\pi}{2})$ like below : (Re?)Install Ubuntu on a Dell laptop that had Ubuntu preinstalled I have Dell Laptop that is 15 5567 7th Generation. So it was maybe pre-installed as Dell says and I can see in the product information that this laptop is Ubuntu built in and based not Windows.  So I want to get my Ubuntu OS again. How can I do that? MySQL 5.5.16 allows anonymous connections Apparently, I can connect to MySQL (at least from my localhost) without having to provide any username or password. I can even put anything as username, as long as the password is empty. I have access to the information_schema and test databases. I can create tables. If I run SELECT USER() it returns the proper value randomstring@localhost, where the random string is whatever I used for username when I connected.  The mysql.user table contains root@localhost, root@127.0.0.1, @localhost and pma@localhost. I manually set encrypted passwords to all the records (UPDATE user SET password=...) and only root has any privileges, the other two records have "N" for all privileges. That record with the empty username looks suspicious, but I don't think it has anything to do with this and I think it was there from the beginning.  To make matters worse, if I add a user with a password, I can only connect using empty string as password (just like if I put anything as username). If I try to connect using the username I created and password I supplied when creating it (CREATE USER .. IDENTIFIED BY ..) it doesn't work.  Does anyone know what is wrong and how I can fix this?  Note: I am using MySQL 5.5.16 for Windows, provided by the XAMPP package. Should I use 'was' or 'were' in this example?     I was always delighted when my brother or one of my sisters was/were asked to do them. I'm trying to give the best experience to users of a very huge system (like a CRM). It has a lot of forms and much of these have a lot of fields. My doubt is about if I should use a single column form (which raises too much vertical scrolling), or a two columns form (which needs less vertical scrolling and uses more horizontal white space) and a last one with four columns (which has few scrolling and uses almost whole white space to try to keep most of the fields above the fold).  It's important to say that our clients hate scrolling, and they always ask why we don't use the horizontal white space when we present a one column form).  So I'm little bit confused about it, because a lot of UX studies and good practices recommend to do not use/avoid multicolumn forms but the clients most of times ask multi column forms.  Our clients are very used to desktop programs and not everybody is very familiar with web based systems.  Below follows some possibilities I would like to share to illustrate an example of a complex form in the system with the three possibilities I mentioned:    In the example above I'm using the one column form (most recommended in UX studies), but with a very long vertical scroll.    In the second example I tried to reduce vertical space by using two columns.    This is the client's favorite one, 4 columns using white space and trying to keep everything above the fold.   The lengths of fields are based on the average of characters amount for each field.   I would like to know your opinion about the best approach to this case. Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip? I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance.  Am I correct?  . Could any one give an example of a bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$?  Thank you. Contraction mapping in the context of $f(x_n)=x_{n+1}$. The Many Memes of Meta Catchphrases and concepts that spread from person to person are known as [memes], which, courtesy the Internet, can now explode across the Earth like a highly contagious virus (hence &quot;going viral&quot;). As with their real-life counterparts, some infectious diseases are global (pandemic), while others are endemic to specific regions. Stack Overflow, and now even more predominantly Meta Stack Exchange, have seen more than their fair share of these pathological social constructs spread through the user base. They are now ingrained units of our collective culture as SOpedians (a term which I hate, by the way). Just as travelers' immune systems can be assaulted by new diseases in new places, new users are increasingly likely to be miffed by an ingrained meme and left sitting scratching their heads. I therefore propose that this space be used to document the memes endemic to Stack Exchange's culture. Each meme should be listed in a separate answer and I hope that we as a community will be able to provide greater context to each one. Please actually explain each meme in a way understandable to those not already in the know. Especially considering that a lot of these memes aren't really understandable to newer users who weren't around in the early years of the network, or are based on system features that no longer exist.  On other Stack Exchange sites          [memes]: Where can I find a standalone installer for Windows 7 Service Pack 1? How do I create an empty array/matrix in NumPy? I can't figure out how to use an array or matrix in the way that I would normally use a list. I want to create an empty array (or matrix) and then add one column (or row) to it at a time.  At the moment the only way I can find to do this is like:  mat = None for col in columns:     if mat is None:         mat = col     else:         mat = hstack((mat, col))   Whereas if it were a list, I'd do something like this:  list = [] for item in data:     list.append(item)   Is there a way to use that kind of notation for  arrays or matrices? How to upgrade to GNOME 3.30 on Ubuntu 18.04.1 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? How can I find out which apps I have already downloaded on my iPhone? When you attempt to download an app that costs money, you will not be charged if you already bought the app. After you press buy and enter your iTunes password, it will say "You have already purchased this item. To download it again for free, select OK."  The problem is that I deleted hundreds of apps from my phone, some of which were paid for. Later on I might find an app I like but notice that it costs money. It might be an app I had already paid for, or an app which I got when it was free.  How can I know if I tap the buy button if I will be charged for the app or not?  In other words, how can I know if I owned a previous version of an app before? What is the most CPU efficient way to ensure that NumLock is on? Situation: I have a script watching over NumLock status, well not really watching, but turning it On every 1 second. The script is running in the background.  Reasoning: I often accidentally turn off NumLock. And I have no indicator of NumLock status on the keyboard.  OS, DE, DM, WM, xmodmap:  :  $ lsb_release -a  No LSB modules are available. Distributor ID: LinuxMint Description:    Linux Mint 18 Sarah Release:    18 Codename:   sarah   :  echo $DESKTOP_SESSION  cinnamon   :  cat /etc/X11/default-display-manager  /usr/sbin/mdm   :  wmctrl -m | head -n 1  Name: Mutter (Muffin)   :  xmodmap -pm  xmodmap:  up to 4 keys per modifier, (keycodes in parentheses):  shift       Shift_L (0x32),  Shift_R (0x3e) lock        Caps_Lock (0x42) control     Control_L (0x25),  Control_R (0x69) mod1        Alt_L (0x40),  Alt_R (0x6c),  Meta_L (0xcd) mod2        Num_Lock (0x4d) mod3       mod4        Super_L (0x85),  Super_R (0x86),  Super_L (0xce),  Hyper_L (0xcf) mod5        ISO_Level3_Shift (0x5c),  Mode_switch (0xcb)   My original Bash script follows:  #!/bin/bash  while true do    numlockx on    sleep 1s  done   As you can see, the script does not care about current status of NumLock. It just keeps turning it on.  Goal: I would like to make the script at least somewhat CPU efficient.  Question: What is the most CPU efficient way to ensure that NumLock is On in Linux (Mint 18)? What is the difference between Python's list methods append and extend? Is the wave-particle duality a real duality? I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' that everything is made up out of particles, whether those are photons, electrons, or maybe even strings. That light for example, also shows wave-like properties, why does that even matter? Don't we know that everything is made up of particles? In other words, wasn't Young wrong and Newton right, instead of them both being right? Start codon AUG also codes for methionine and without start codon translation does not happen. And even the ambiguous codon GUG codes for methionine when it is first. So does this mean that all proteins start with methionine as the first amino acid. Can black holes be created on a miniature scale? How can I modify the advanced search form when my hook runs too early? I'm using  to modify the content of the form on the search page &mdash; I want to remove the "phrase" and "not" fields, and restrict the "only of the types" checkboxes to a hand selected list of types.  I have the following code, which is being called and which I think should work:  function MYMODULE_form_search_form_alter(&amp;$form, &amp;$form_state, $form_id) {     unset($form['basic']);     unset($form['advanced']['keywords']['phrase']);     unset($form['advanced']['keywords']['negative']);     unset($form['advanced']['type']);     $form['advanced']['type'] = array(         '#type' =&gt; 'checkboxes',         '#title' =&gt; t('Only of the type(s)'),         '#options' =&gt; array(             'blog' =&gt; 'Blog entry',             'event' =&gt; 'Event',             'news' =&gt; 'News article'         )     );     // print_r($form);     // die; }   Except  gets to the search form after my form alter hook runs, so I don't get a chance to modify any of the form elements that it's adding.  I'm running Drupal 7.22.  How can I modify the advanced search form when my module hook runs before the hook that defines the advanced search form?