I found this on old CPU motherboard circuit and find its interesting.  What is the purpose of that pattern? is it only for aesthetic or is there something else? I only seen the same pattern on bluetooth module rf antenna.
I've seen many boads with weird zig-zag shaped tracks just like the one below. Why are they designed like that?
echo "#!" fails -- "event not found" While watching  I noticed a very characteristic camera shot. At a scene where the main character, Wendy, sits in her room at the computer (watching the supposedly foretelling fotos), her sister talks to her from the outside (asking if she can have the camera/fotos). There is a certain camera shot, where on the left side a frontal close-up of Wendy's face is shown, while on the right side you see her sister standing in full height inside the open door.    This shot immediately struck me as being somehow characteristic and out of place and infused feelings to me of some kind of older Hitchcock or Brian De Palma thriller or something the like. I also think to remember of having seen this kind of shot or something similar used in , where Jessica Lange is shown in front of the dresser talking to Nick Nolte who stands in the door or father away.  I would like to know if this technique has a certain name or theory behind it and where its origins lie, or if there is any particular director or movie who made this famous. It may be even that Final Destination 3 uses this especially in reference to some director or movie. Keeping an updated balance (Accounting) I have been struggling trying to find a way to properly and reliably maintain a balance for accounts in an order/payment system.  Currently, the process consists of three tables. Below example is very simplified but gets the point across.  Table one contains the account ID, name, total paid, total orders, balance etc.  Table two contains payments, date, the account ID (FK) and amount.  Table three contains orders, date, the account ID (FK) and amount.  Calculating the balance is of course as easy as  SELECT SUM(payments.AMOUNT) FROM payments WHERE ID = [account] SELECT SUM(orders.AMOUNT) FROM orders WHERE ID = [account]   Followed by some simple addition/subtraction math:  UPDATE accounts SET BALANCE = [balance] WHERE ID = [account]   All good - the problem is - how do I maintain this over let's assume years of activity and many, many transactions?  Currently the accounts table is updated every single time a transaction is made, meaning the above three statements run every time. There is of course an index on the ID column in all three tables, and everything is fast and neat for now, but I work with less than 100,000 transactions, meaning everything fits into the RAM and basically all I throw at the database gets executed immediately. Over time this will change, of course - so how do I handle this?  Is it better to mark the accounts as "dirty" and process balancing in a batch job later, or can I keep updating the balance real-time even when I reach the point where the orders and payments tables will not fit into the RAM?  Do I need to segment the orders and payments and "lock" everything before a given time, such as before last calculation? (I would rather not). I ask because then I could do a SUM WHERE DATE > [last lock timestamp] and update with UPDATE BALANCE = [balance] + [value for last lock] and prevent the problem from outgrowing resources.  I don't need a running balance for each transaction. That's all I can find results for when I try to research this problem. I just care about the total amount paid, the total amount ordered and the balance of accounts.  Why don't I calculate on the fly when I need the balance, you ask? Because one must be able to query the system and ask "Which of my (let's say) 50.000 accounts have a balance below 0?" - something we cannot do easily if we do not store the balance with every account. Are $10\times 10$ matrices spanned by powers of a single matrix? Summability vs Unconditional Convergence I'm reading that summability and unconditional convergence are the same. (At least if the index set is countable, so unconditional convergence makes sense.)  Then unconditional convergence is nothing else than convergence of the net of all rearranged partial sums. Thus uniqueness of the limit becomes fairly easy as the limit of every net in a Hausdorff space is unique.  But the usual proof deals with separating functionals on Banach spaces, which is a much more serious technique. So I think there must be a hook in my reasoning. Can somebody resolve this issue? Thanks a lot!  Best Regards, Freeze_S I just discovered Matlab's factor()-function, and I randomly typed in 20081294819, and to my surprise it only had two factors (5099 and 3938281)! I had expected many more factors for such a big number and wondered how normal this was. The following is what I've done in my investigation so far.  In the first figure below, I have plotted the probability that some number below $10^k$ has $m$ indistinct prime factors.  The second figure shows the evolution of the probability of finding a number with $m$ indistinct prime factors as the numbers one is looking at grows, i.e. it is just another way to visualize the same data. I have left out all points of zero probability.  If one looks at the first part of the figure, it seems that the peak of the curve for some $k$ shifts toward higher $m$ as $k$ grows.   My first question is this: Does this behavior (i.e. the peak shifting toward higher $m$ as $k$ grows) continue indefinitely, or will the peak stabilize at some point? The latter seems unlikely but I can't be sure.  My second question is this: Approximately how fast does the peak-value $m_{peak}$ move as $k$ grows?  I briefly looked at the , but this involves distinct primes and I don't really know much number theory, so any help would be greatly appreciated! How often did Gandalf return to Hobbiton after the events of The Hobbit? It has been a while since I read the Lord of the Rings novels (don't have a copy at the moment) but I seem to recall he went to Hobbiton at least once, as the young hobbits were always excited to see him.   Did he travel there often? Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$ Given measure space $(X, \mu)$ and measurable function $f$. If $p \in (0, +\infty]$, below are the facts I know about $\Vert f \Vert_p$:  (log convex in $\frac 1 p$) $\forall p_1, p_2\in (0, +\infty] \text{ such that } p_1 &lt; p_2. \forall t \in(0, 1), \text{ let } \frac 1 p = \frac t {p_1} + \frac {1-t} {p_2}$, then $\Vert f \Vert_p \le \Vert f \Vert_{p_1}^t\Vert f \Vert_{p_2}^{1-t}$ ($0\cdot(+\infty)$ is defined to be $0$). (lower semi-continuity) $\forall p_0 \in (0, +\infty], \liminf_{p\to p_0}\Vert f\Vert_p \ge \Vert f \Vert_{p_0}$. If $0&lt;\mu(X) &lt; +\infty$, then $ \Vert f \Vert_p/\mu(X)^{\frac 1 p}$ is monotone increasing in $p$, combine it with (2) we get $\lim_{p\to p_0-}\Vert f\Vert_p = \Vert f \Vert_{p_0}$.  From (1) we know the set of $p$ such that $\Vert f \Vert_p &lt; +\infty$ is an interval $I$ (possibly empty or a singleton).  If $I \not\in a = \inf I$ and $a \neq 0$, from (2) we know $\lim_{p\to a+} \Vert f \Vert_p = +\infty$. If $I \not\in b = \sup I$, then $\lim_{p\to b-} \Vert f \Vert_p = +\infty$.  From (1) and the dominated convergence theorem we know that if $I \ni p_0 \neq \inf I$ and $p_0 &lt; +\infty$, then $\lim_{p\to p_0+} \Vert f \Vert_p = \Vert f \Vert_{p_0}$. If $I \ni p_0 \neq \sup I$, then $\lim_{p\to p_0-} \Vert f \Vert_p = \Vert f \Vert_{p_0}$.  If $I$ is nondegenerate and $+\infty \in I$, then $\lim_{p\to +\infty}\|f\|_p = \|f\|_{\infty}$.  If $\inf I = 0$, from (1) we know $\lim_{p\to 0+}\|f\|_p$ exists.   Question: How $\Vert f \Vert_p$ behaves when $p$ is the endpoint of $I$? To be more precise, assume $I$ is nonempty. Let $p_0 = \sup I$ (only right endpoint is considered for simplicity):  $p_0\in I$ or $p_0 \not\in I$? Can $I$ be a singleton? What if $p_0 = +\infty$? What if $0&lt;\mu(X) &lt; +\infty$?  Please also notify me if there is any mistake above. Is it okay to use Stack Overflow as the support forum for a product or project? I recently saw a question about a problem (or possible bug) with some product on Stack Overflow. At first, I wanted to suggest that the asker post his question to that product's support forum.  When searching for the URL of that forum, I noticed that the product developer closed its support forums and now advises users to post all their questions on Stack Overflow instead.  Is this within the intended use cases of Stack Overflow, or is this abuse? I'm looking for a way to search files where two word instances exist in the same file.  I've been using the following to perform my searches up to this point:  find . -exec grep -l "FIND ME" {} \;   The problem I'm running into is that if there isn't exactly one space that between "FIND" and "ME", the search result does not yield the file.  How do I adapt the former search string where both words "FIND" and "ME exist in a file as opposed to "FIND ME"?  I'm using AIX. I followed the instructions and got success response but I didn't receive email.  Then I used the id to get Email Status and got 404 error.  Here is my json :  POST :   {     "To": {         "Address": "example@gmail.com",         "SubscriberKey": "example@gmail.com.tw"     },     "Options": {         "RequestType": "ASYNC"     } }   GET : {id}  Please let me know how I can resolve the issue. I am new to Force.com and trying to learn some concepts.  Currently I am using Single Email Message to send my emails, but I need to change that to mass email, but I don't quite understand how to do that.   I have also created a Visualforce email template, which I would like to use, but it doesn't seem to work.   It would be great if someone could help me out.  //email_disease_map contains pairs of email address and disease ID for (Id id : email_disease_map.keySet())   {     Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();     String[] defaultAddresses = new String[] {'id@test.com'};      List&lt;String&gt; toAddresses = new List &lt;String&gt; (email_disease_map.get(id));      if (!toAddresses.isEmpty())       {         //set addresses for email to be sent         mail.setToAddresses(defaultAddresses);         mail.setCcAddresses(toAddresses);         mail.setTemplateId(Notification);         //set up remaining email         mail.setReplyTo('test@mail.com');          mail.setSenderDisplayName('Ms Test');          Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });       }  } How do I suppress the whitespace above an equation block at the page top? How do I suppress the whitespace above the equation block at the page top ? It is added to the top margin, and I don't want that to happen. I know that \abovedisplayshortskip controls this for the whole document, but how can I change this for this particular equation block and NOT for any others ? Negative vspace doesn't work.  \documentclass[pdftex,12pt,a4paper,english,dutch,leqno]{article} \usepackage[top=1cm,right=1cm,bottom=1cm,left=1.5cm,noheadfoot]{geometry}         \usepackage{babel} \usepackage{amsmath} \usepackage{amssymb} \usepackage{empheq}  \begin{document}  \abovedisplayskip=6pt \abovedisplayshortskip=3pt % This should NOT be changed \belowdisplayskip=6pt \belowdisplayshortskip=3pt  \begin{equation*} \left.\begin{array}{r} a_{31}'=a_{11}\cdot a_{31}-a_{31}\cdot a_{11}=0\\ a_{32}'=a_{11}\cdot a_{32}-a_{31}\cdot a_{12}\\ a_{33}'=a_{11}\cdot a_{33}-a_{31}\cdot a_{13}\\ a_{34}'=a_{11}\cdot a_{34}-a_{31}\cdot a_{14}\\ b_{3}'=a_{11}\cdot b_{3}-a_{31}\cdot b_{1} \end{array}\!\!\right\} \Longrightarrow\; \begin{matrix*}[l] \text{Pseudo-code :}\\ a_{11}\cdot b_{3}-a_{31}\cdot b_{1}\mapsto b_{3}\text{.}\\ \forall\;i\in\{4,3,2,1\} : a_{11}\cdot a_{3i}-a_{31}\cdot a_{1i}\mapsto a_{3i}\text{.} \end{matrix*} \end{equation*}  \end{document} I have a DisplayPort based monitor, and a laptop with a DP out.  I recently got a second laptop with HDMI out, and went looking for a HDMI -> DP converter.  I was very surprised to find that such a thing effectively doesn't seem to exist.   and the  seem to imply that it's just not possible to go HDMI -> DP, without a very expensive converter box (not just an adaptor).  However, I can't find anything that explains why this is the case.  Is DP designed to be backwards compatible but can't interpret HDMI?  Is it a case of HDMI-quality signal not being high enough quality to be convertible?  Some other reason?  Note that this question is not looking for an adaptor - I'm looking for the underlying cause of the lack of them. I'd like to create a popup list on one of my Visualforce pages, for a user to select from a list of OrgWideEmailAddress records.  My goal is to limit the list to only those records that they're allowed to use.  I'm going to save the selection for use in later automatic emails.  Based on what I've read, I won't be able to send emails to certain OrgWideEmailAddresses:   The address hasn't been verified yet.  I don't see any fields in the schema that appear to show verification state. The address is only available to profiles that the user isn't a member of.  I don't see where the profile list is stored for each record.   Some of my problem could just be due to not understanding the standard objects so well, and perhaps there's a way to get at this through UserInfo, or by making my query on the User object which may have a child relationship to OrgWideEmailAddress since it's listed in the schema viewer of the Force.com IDE.  Here's the test code I'm working with:  for (OrgWideEmailAddress addr : [SELECT DisplayName, Address          FROM OrgWideEmailAddress ORDER BY DisplayName]) {     System.debug( addr.DisplayName + ' &lt;' + addr.Address + '&gt;'); }   I tried creating a new Messaging.SingleEmailMessage and then calling setOrgWideEmailAddressId() on it with each OrgWideEmailAddress Id, in hopes that invalid Ids would throw an exception, but to no avail.  My goal is to modify the test code to provide just the subset of records that the current user will be able to use. Log of mounted/unmounted devices in Unix No Sound (Dummy Output) error Ubuntu 19.10 How does password salt help against a rainbow table attack? I'm having some trouble understanding the purpose of a salt to a password.  It's my understanding that the primary use is to hamper a rainbow table attack.  However, the methods I've seen to implement this don't seem to really make the problem harder.  I've seen many tutorials suggesting that the salt be used as the following:  $hash =  md5($salt.$password)   The reasoning being that the hash now maps not to the original password, but a combination of the password and the salt.  But say $salt=foo and $password=bar and $hash=3858f62230ac3c915f300c664312c63f.  Now somebody with a rainbow table could reverse the hash and come up with the input "foobar".  They could then try all combinations of passwords (f, fo, foo, ... oobar, obar, bar, ar, ar).  It might take a few more milliseconds to get the password, but not much else.  The other use I've seen is on my linux system.  In the /etc/shadow the hashed passwords are actually stored with the salt.  For example, a salt of "foo" and password of "bar" would hash to this: $1$foo$te5SBM.7C25fFDu6bIRbX1.  If a hacker somehow were able to get his hands on this file, I don't see what purpose the salt serves, since the reverse hash of te5SBM.7C25fFDu6bIRbX is known to contain "foo".  Thanks for any light anybody can shed on this.  EDIT:  Thanks for the help.  To summarize what I understand, the salt makes the hashed password more complex, thus making it much less likely to exist in a precomputed rainbow table.  What I misunderstood before was that I was assuming a rainbow table existed for ALL hashes. I know that $re^{i\theta} = x + iy$ for any complex number $x + iy$ by Euler's formula. How do you calculate relative and global phase? What do I set the 'Opens with...' property to in order to get the system to run .bat files again (when they are double-clicked)?  Somehow my boss convinced his workstation that the handler for .bat files was supposed to be Word. Now, when double-clicking .bat files, they're opened up in Word.