What are waves? I am layman when it comes to physics, but I cannot understand what is often meant when waves are discussed. I understand physical waves, e.g. water, as a type of behaviour of some fluid or medium. So in this picture there's a bunch of molecules moving in a certain fashion. But I fail to understand the concept of waves when is talked about radio waves or even worse when I read about the double slit experiment and particle wave duality. What are these wave made off / what medium do they live in?
How do electromagnetic waves travel in a vacuum? This is perhaps a total newbie question, and I will try to formulate it the best I can, so here it goes. How does an electromagnetic wave travel through for example, the vacuum of space?   I usually see that waves are explained using analogies with water, pieces of rope, the strings of a guitar, etc, but it seems to me that all those waves need a medium to propagate. In fact, from my point of view, in those examples the wave as a "thing" does not exist, it's just the medium that moves (involuntary reference to The Matrix, sorry).   But in space there is no medium, so how does a wave travel? Are there free particles of some sort in this "vacuum" or something? I believe , so supposedly there isn't a medium for the wave to travel through.   Moreover, I've seen other answers that describe light as a perturbation of the electromagnetic field, but isn't the existence of the field, potential until disturbed? How can it travel through something it does not exist until it's disturbed by the traveling light in the first place? (this last sentence is probably a big misconception by me).
SUB-TREE WITHIN A TREE in MySQL  In my MYSQL Database COMPANY, I have a Table: Employee with recursive association, an employee can be boss of other employee. A self relationship of kind (SuperVisor (1)- SuperVisee (∞) ).     Query to Create Table:    CREATE TABLE IF NOT EXISTS `Employee` (   `SSN` varchar(64) NOT NULL,   `Name` varchar(64) DEFAULT NULL,   `Designation` varchar(128) NOT NULL,   `MSSN` varchar(64) NOT NULL,    PRIMARY KEY (`SSN`),   CONSTRAINT `FK_Manager_Employee`                 FOREIGN KEY (`MSSN`) REFERENCES Employee(SSN) ) ENGINE=InnoDB DEFAULT CHARSET=latin1;   I have inserted a set of tuples (Query):    INSERT INTO Employee VALUES   ("1", "A", "OWNER",  "1"),     ("2", "B", "BOSS",   "1"), # Employees under OWNER   ("3", "F", "BOSS",   "1"),   ("4", "C", "BOSS",   "2"), # Employees under B  ("5", "H", "BOSS",   "2"),   ("6", "L", "WORKER", "2"),   ("7", "I", "BOSS",   "2"),   # Remaining Leaf nodes     ("8", "K", "WORKER", "3"), # Employee under F        ("9", "J", "WORKER", "7"), # Employee under I        ("10","G", "WORKER", "5"), # Employee under H   ("11","D", "WORKER", "4"), # Employee under C  ("12","E", "WORKER", "4")     The inserted rows has following Tree-Hierarchical-Relationship:                A     &lt;---ROOT-OWNER         /|\                     / A \               B     F      //| \    \              // |  \    K        / | |   \                       I  L H    C         /     |   / \  J     G  D   E   I written a query to find relationship:    SELECT  SUPERVISOR.name AS SuperVisor,          GROUP_CONCAT(SUPERVISEE.name  ORDER BY SUPERVISEE.name ) AS SuperVisee,          COUNT(*)   FROM Employee AS SUPERVISOR    INNER JOIN Employee SUPERVISEE ON  SUPERVISOR.SSN = SUPERVISEE.MSSN  GROUP BY SuperVisor;   And output is:    +------------+------------+----------+ | SuperVisor | SuperVisee | COUNT(*) | +------------+------------+----------+ | A          | A,B,F      |        3 | | B          | C,H,I,L    |        4 | | C          | D,E        |        2 | | F          | K          |        1 | | H          | G          |        1 | | I          | J          |        1 | +------------+------------+----------+ 6 rows in set (0.00 sec)   [QUESTION] Instead of complete Hierarchical Tree, I need a SUB-TREE from a point (selective) e.g.: If input argument is B then output should be as below...  +------------+------------+----------+ | SuperVisor | SuperVisee | COUNT(*) | +------------+------------+----------+ | B          | C,H,I,L    |        4 | | C          | D,E        |        2 | | H          | G          |        1 | | I          | J          |        1 | +------------+------------+----------+      Please help me on this. If not query, a stored-procedure can be helpful. I tried, but all efforts were useless! Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist? Does a log transform always bring a distribution closer to normal? I have a highly right skewed data set with a large range of values (from 1 ~ 10^6) (can't share the actual data for work related reasons).   When I plot the log of the data instead, the distribution looks a lot more like a normal distribution.   Have I stumbled on a meaningful insight in the data set, or is just a general property of the log transform that it brings the distribution closer to normal? Singular verb after two noun phrases joined by "and" that can be thought of as a single thing I am having trouble with the following sentence:      "The complexity and diversity of the new platforms is worrying us."   If "complexity" and "diversity" constitute two subjects, then the verb should presumably be "are"; however, the sentence feels more natural with "is". Is this correct? Is there a linguistic term for this occurrence?    The following questions address the general topic of compound subjects, but not specific cases like this:             And the following question seems to have somewhat inconclusive answers:         So this question is not really a duplicate of these three. Are there number systems corresponding to higher cardinalities than the real numbers? App question timer shouldn't kick in until submission I attempted to ask a question using the iOS app, but it was rejected due to lack of a required tag. On adding the tag I found that I wasn't permitted to submit the question for another 60 seconds, even though this wasn't a new question.  Is this timer intentional, or should it not kick in for edits of questions not actually accepted by the site? Storable Action - System.LimitException: Too many DML statements: 1 @AuraEnabled(cacheable=true) public static String  deleteContacts(List&lt;String&gt; contactIds) {     List&lt;Contact&gt; returnList = new List&lt;Contact&gt; ();     String query = ' SELECT Id,Name, LastName,Department,MobilePhone, Email FROM Contact WHERE id IN : contactIds ';     for (Contact thisContact:  Database.Query(query)) {          returnList.add(thisContact);     }     try {       delete returnList;       return'deleted successfully';     }     catch(Exception ex){        return 'Problem occoured';     }  }  JS Method deleteSelected(){     deleteContacts({         contactIds :this.selectedIds     })      .then(result =&gt; {         this.dispatchEvent(             new ShowToastEvent({                 title: 'Success',                 message: result,                 variant: 'success',             }),         );         return refreshApex(this.getContactList, { searchKeyWord: '$searchKeyWord' });     })     .catch(error =&gt; {         this.error = error;     }); Number of edges of any spanning tree of a graph $G$ coming from a subgraph of $G$ Consider a simple undirected, unweigthed graph $G=(V,E)$ and its edge-induced subgraph $G^{*}=(V^{*},E^{*})$. Suppose that $G$ and $G^{*}$ have $c$ and $c^{*}$ connected components, respectively. Is it true that any spanning tree of $G$ has exactly  $$|V^{*}|-\min\{c^{*},c\}$$  edges from $E^{*}$? Could somebody give a proof/counterexample? Thank you for the help! Chat is an offshoot of the main site, and using it is  during their time here.  Chat is our place for:        Real-time collaboration   Meeting fellow members of the community   Less structured, casual (but still roughly on-topic) conversation      Our chat system exists to serve the main site; users of each site can gather and commune with each other.  When in chat, we expect all users to abide by our  policy, which means that we expect community members to treat each other with respect.    While it is a place where the community can go to interact on a more casual level, chat still needs to be moderated by the community and there are tools in place to help with the moderation. This raises a few questions, that are addressed here: Google street view URL Hi I have the address of a property and my application can launch a browser to go to . If a good match is found it will take it directly there. Is there any thing I can append to the url to make it switch to streetview without having the exact coordinates? I dont't want to code any javascript or flash. I have a couple of big text files and in the file UNIQS.txt I have a list of strings to grep from another file. The code I use is  grep -f UNIQS.txt EEP_VSL.uniqs.sam &gt; UNIQ_templates.sam   which does nothing - the file generated is empty. But when I do  grep -F -f UNIQS.txt EEP_VSL.uniqs.sam &gt; UNIQ_templates.sam   it works correctly. This confuses me because I didn't think grep would interpret the entries in UNIQS.txt as regexp patterns without quotes and slashes and so on being in the file (which there aren't). Is it the case in general that if you are getting the patterns from a file then it will automatically think that they are regexp patterns?  Edit: In the UNIQS.txt file, there are newline separated strings of the form  HWI-ST365:215:D0GH0ACXX:2:1101:10034:186783   (called template names) and the file EEP_VSL... tab separated columns, with about 14 columns and the first column is the template name, so basically I want to extract the line corresponding to each template in the file. How to recover files from dead windows using dos? I'll preface this by saying I'm very new to Blender - I'm trying to put a bevel on an edge, looks something like this:    As you can see, the vertical side is much longer than the horizontal side.  When I apply to bevel to the edge there, the bevel stretches proportionally - so there's 'more' bevel on the longer side.  I want to bevel without any 'ratio' like that - just a 45-degree bevel, if that makes any sense.  Do I have to put in a loop cut to make the side lengths equal?  I tried using a sub-surf modifier, but it applies on a bunch of nearby edges, when I just want to round this one corner. How to create a Wi-Fi Hotspot (in Access Point mode)? My Android device screen got broken and I can't see what I'm doing. That's the only wrong thing with my device, the rest is apparently working OK. Is there any way to send my device screen to my computer? I don't want to work blindly anymore! It’s a story of a female protagonist who has a harsh life. Just as she is about to die, she time travels back into her young self. To avoid the future she already lived, she decides to gets strong by learning swordsmanship. After a while, she joins the army under the command of a prince who wears an eye patch. She is quite OP, and helps the prince. It was kind of a medieval setting manga, with dukes and earls and count types. Time is when the use of sword and magic is prominent. Ubuntu Software doesn't open in Ubuntu 20.04 If i click on Ubuntu Software, it doesn't open. I have a fresh install of Ubuntu 20.04. I tried try to upgrade all packages, but it doesn't fix this problem.  If I try to run killall software-center there is no process with this name, and software-center returns command not found. If I try to reinstall it with apt I have these results:  $ sudo apt-get --purge --reinstall install software-center Reading package lists... Done Building dependency tree        Reading state information... Done Package oracle-java8-installer is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'software-center' has no installation candidate Why am I getting 50V at a light when the switch is off? How to cross-reference items in description lists? Every now and then I use the description list environment  \begin{description} \item[foo]  foo is good \item[bar]  bar is bad \end{description}   to create lists with non-numerical labels. Unfortunately the description list does not support the label-reference pair as normal latex: i.e. if I write  \begin{description} \item[foo] \label{foo} foo is good .... \end{description} .... For good things (see, for example \ref{foo})...    the reference does not point to the item in the list. Instead it points to the closest environment that supports labeling (usually the subsection). So instead of showing the text foo (in boldface), it shows something like 2.2.1 (the subsection corresponding to where the description environment is sitting).  My question: is there a way or a package which allows references to description list items? My current work-around is to just type the text myself in the spot (since I named it myself, and it is not numbered, the formatting is unlikely to change the label =). But one of the good things about the label/reference pairs in latex is the implementation in pdflatex that allows in PDF hyperlinks between references and the objects referred to, this I cannot replicate myself.   Edit: let me rephrase my question. The primary goal is not to display \ref to something other than what LaTeX thinks the \label is. There are many ways to deal with it, some of which outlined in Michael Underwood's helpful answer below. What I am looking at is whether there exists an implementation of a list environment which is like the built-in description environment in that the displayed "title" for the list item is completely customized, while having support for \labels. (The built-in description environment does not support \labels, whereas the built-in enumerate environment does not support customized "title"s.) The enumitem package adds some customizability to the environments, but as far as I can tell it doesn't support exactly what I want. Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$ $M$ is a $3 \times 3$ matrix such that $\det(M)=1$ and $MM^T=I$, where $I$ is the identity matrix. Prove that $\det(M-I)=0$  I tried to take $M$ $=$ $$ \begin{pmatrix}         a  &amp;b &amp; c \\         d &amp; e &amp; f \\         g &amp; h &amp; i         \end{pmatrix} $$   but its expansion is too long.