How STL Containers Instantiate For User Objects
Why can templates only be implemented in the header file?
SC2272-M4 Behaviour when using relay SRD-05VDC-SL-C 5V DC I'm currently encountering a problem when using a relay switch with a 5v receiver. When using the same receiver with a row of LEDS it works flawlessly. I've noticed that the relay keeps making the switching noise over and over like I'm pressing the transmitter really fast apart from the fact I'm not. Also, when the transmitter is moved closer to the receiver from 20" to around 1" the problem stops. Below is some circuits to help show you my setup.  Any help appreciated thanks.  Setup Specs   USB 5v DC (2AMPS) Receiver (XY-DJM-5V - SC2272-M4) Relay (SRD-05VDC-SL-C 5V DC) Transmitter (XY-04) Diode (1N4001) Transistor (2N2222A) Resistor (1.8K Ohms)          &ndash; Schematic created using   Antenna Signal Workaround or Booster  I believe this issue is related to wireless signal on D0. Basically above 20" inches the output to the relay drops from 5.05v to 0.5v and is obviously causing the problem. I think I need to boost the signal or replace the transistor with something that triggers at low and high current but have no clue. Any help appreciated, I'm new at this.  Board Setup If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$ How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence Let $F_n$ be the Fibonacci sequence where  $F_0$ = 0  , $F_1$ = 1 and  $F_n$ = $F_{n-1}$ + $F_{n-2}$.                   I want to prove the following by induction. $$\sum_{k=1}^{n}F_k = F_{n+2}-1$$ Here is what I have so far.  Can anybody tell me if I am right?  Base case = n=1  $F_k$ = 1 = LHS  $F_{1+2}$ - 1 = 2 - 1 = 1 = RHS  Statement is true for n=1.  Assume statement is true for n=i.  $$\sum_{k=1}^{i}F_k = F_{i+2}-1$$  Prove statement is true for n=i+1.  $$\sum_{k=1}^{i+1}F_{k} = F_{((i+1)+2)}-1$$  $F_1$ + $F_2$ +...+ $F_i$ + $F_{i+1}$ = $F_{((i+1)+2)}-1$  $F_{i+2}$ - 1 + $F_{i+1}$ = $F_{((i+1)+2)}-1$  $F_{((i+1)+2)}-1$ = $F_{((i+1)+2)}-1$  Statement holds for n=i+1 Why is BigDecimal returning a weird value? Outlier Detection on skewed Distributions Every time I try to create a table using MySQL Workbench 6.3 CE it adds "broken" comments at the end of the script.  Example:  I am trying to create a table called "user". This is what the table should look like:   However when I click the apply button, the script generates incorrectly:  CREATE TABLE `user` (   `userid` INT NOT NULL AUTO_INCREMENT COMMENT '',   `record_status` INT NOT NULL DEFAULT 1 COMMENT '',   `createdby` VARCHAR(75) NOT NULL COMMENT '',   `createddate` DATETIME NOT NULL COMMENT '',   `updatedby` VARCHAR(75) NULL COMMENT '',   `updateddate` DATETIME NULL COMMENT '',   `username` INT NOT NULL COMMENT '',   `password` VARCHAR(75) NULL COMMENT '',   `firstname` VARCHAR(75) NULL COMMENT '',   `lastname` VARCHAR(75) NULL COMMENT '',   `email` VARCHAR(75) NULL COMMENT '',   `facebook_userid` VARCHAR(75) NULL COMMENT '',   `email_verified` VARCHAR(75) NULL COMMENT '',   PRIMARY KEY (`userid`, `username`)  COMMENT '');   The comment in this line should not be there, so the code should be:   PRIMARY KEY (`userid`, `username`));   and the code executes when I paste it into an editor and remove this comment. However I create massive databases daily. (Each with +- 15 tables). I can't keep doing this for each table as it is time consuming.  How can I disable this feature that adds the comments to the script? I don't need them in my databases Find the value of : $\lim_{n\to\infty}\prod_{k=1}^n\cos\left(\frac{ka}{n\sqrt{n}}\right)$ Space of bounded continuous functions is complete I have lecture notes with the claim $(C_b(X), \|\cdot\|_\infty)$, the space of bounded continuous functions with the sup norm is complete.  The lecturer then proved two things, (i) that $f(x) = \lim f_n (x)$ is bounded and (ii) that $\lim f_n \in \mathbb{R}$.  I don't understand why it's not enough that $f$ is bounded. I think the limit of a sequence of continuous functions is continuous and then if $f$ is bounded, it's in $C_b(X)$. So what is this $\lim f_n \in \mathbb{R}$ about? Many thanks for your help. Use of "though" versus "however" Consider the sentence      E-books are on the rise, but they haven't suppressed paper books though.    This usage seems to be quite common, but when I learned English  I was taught to use "however" where I now read "though". My questions on this use of "though" are:     Is this a new trend? Is it restricted to American English? Is "though"  considered more colloquial than "however" ?    And on a syntactic level: Do you put a comma before "though"? What made us think that Earth moves around the Sun? What is the difference between Python's list methods append and extend? What's the difference between the list methods append() and extend()? Is list::size() really O(n)? Recently, I noticed some people mentioning that std::list::size() has a linear complexity. According to  , this is in fact implementation dependent as the standard doesn't say what the complexity has to be. The comment  says:     Actually, it depends on which STL you   are using. Microsoft Visual Studio V6   implements size() as {return (_Size);   } whereas gcc (at least in versions   3.3.2 and 4.1.0) do it as { return std::distance(begin(), end()); } The   first has constant speed, the second   has o(N) speed    So my guess is that for the VC++ crowd size() has constant complexity as Dinkumware probably won't have changed that fact since VC6. Am I right there? What does it look like currently in gcc? If it is really O(n), why did the developers choose to do so? Can you use class features while Polymorphed? More specifically I'm trying to understand if a Barbarian who has been polymorphed, either willingly or not would be able to . However this also applies to things such as , or , anything a player might want to continue to use while no longer themselves.  Many questions specify you're able to rage while Wild Shaped, as  specifies      You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so.   However,  specifies the following,     The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast. It retains it's alignment and personality.   And     The creature is limited in the actions it can perform by the nature of its new form.   Unlike Wild Shape, nowhere does polymorph specify that you retain benefits from your class or race. Does this imply that class abilities do not carry over to polymorphed individuals? RegEx for Javascript to allow only alphanumeric I need to find a reg ex that only allows alphanumeric. So far, everyone I try only works if the string is alphanumeric, meaning contains both a letter and a number. I just want one what would allow either and not require both. You can't see the question owner's special color Can a decision in a node of a decision tree be based on comparison between 2 columns of the dataset? Assume the features in the dataframe are columns - A,B,C and my target is Y  Can my decision tree have a decision node which looks for say, if A&gt;B then true else false? I am looking for a proof possibly using the sandwich theorem and/or Bernoulli's inequality for proving the following statement:  If $x&gt;0$ then $x^{1/n}$ tends to $1$. For example:  "Last week, I found out that NASA stands for 'National Aeronautics and Space Administration.'"  or  "Last week, I found out that NASA stood for 'National Aeronautics and Space Administration.'" how is this possible? I know there is some trick, should someone please explain?! TikZ: Having circle borders only grown to the outside