Does a simulacrum'd creature's statblock include its personality and knowledge/memories?
How do simulacra behave?
Recurrence relation for number of ternary strings that contain two consecutive zeros The question is: Find a recurrence relation for number of ternary strings of length n that contain two consecutive zeros.    I know for ternary strings with length one, there are 0. For a length of 2, there is just 1 (00), and for a length of 3, there are 5 (000,001,002,100,200).    I did a similar problem, finding a relation for the number of bit strings of length n with two consecutive zeros: $$a_n = a_{n-1} + a_{n-2} + 2^{n-2}$$    Since you can add "1" to the end of all the $a_{n-1}$ strings, "10" to all the $a_{n-2}$ strings, and "00" any string of size $n-2$.    For the ternary string problem, I'm pretty sure you would replace the $2^{n-2}$ with $3^{n-2}$, but confused about the other terms of the relation. My guess is that it would have the coefficient $2$ in front of the other terms, since you can add either $1$ or $2$ to the end of $a_{n-1}$ and either $01$ or $02$ at the end of $a_{n-1}$.    So I believe the answer for the relation is: $$a_n = 2a_{n-1} + 2a_{n-2} + 3^{n-2}$$    How does that look? Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$ Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}.$ $f$ is a constant function? Object created by joining several objects doesn't rotate uniformly consistently Aloha.  I'm experiencing a similar problem I had with a prior posting  with another object I created by joining 3 objects that doesn't rotate uniformly consistently.  I tried clearing and applying rotation of individual objects and joined objects to no avail.  I have  as well as object by itself in blend file if you need to see them  Any ideas?  Thanks. How can I manage the "Open with Explorer" button based on user permissions? I write some choice questions into beamer frame, after some research, here is my code:  \documentclass[aspectratio=169]{beamer} \usetheme{Berkeley} \usepackage{tasks,CJK} \begin{document} \begin{CJK*}{utf8}{bsmi} \begin{frame} \transwipe 1.Which one you want to choose? \begin{tasks}[counter-format=tsk[A].,debug=true](4) \task A \task B \task C \task D \end{tasks} \end{frame} \end{CJK*} \end{document}   output with pdflatex:  But I don't want the D choice goto the second line, I want them stay in one line, what should I do? I saw the sentence like     Donald Trump to run for president next month.   in the newspaper on the internet.  But I don't know why we have to use to instead of will.  Is there any rule I don't know?  Can anyone tell me the reason why we should use to in the news? Data inconsistency prohibition if a table refers to another via two many-to-many relationships I have following database design (by =&gt; foreign key constraints are depicted):   Company[id] CompanyRealm[id, company_id=>Company.id]many2many  Project[id, company_id=>Company.id] ProjectRealm[id, project_id=>Project.id, company_realm_id=>CompanyRealm.id]many2many   Problem is that provided database design allows inconsistent data. For example:   Company1(id=1) Company2(id=2) CompanyRealm(id=11, company_id=1) Project(id=33, company_id=2) ProjectRealm(id=44, project_id=33, company_realm_id=11)   (Company can have many Realms, Project belong to Company and  may concern any number of company's Realms)  ProjectRealm refers to two different companies:   Company1 (via CompanyRealm); and Company2 (via Project).    Is something wrong with my DB design? If yes - which prescriptions are violated? If no - how to prevent incorrect data insertion (via constraint? trigger with exception?) Beamer: bold math no longer working I can't find a definitive answer for this. As far as I know, you can't have multiple __init__ functions in a Python class. So how do I solve this problem? Suppose I have a class called Cheese with the number_of_holes property. How can I have two ways of creating cheese objects...  One that takes a number of holes like this: parmesan = Cheese(num_holes = 15) And one that takes no arguments and just randomizes the number_of_holes property: gouda = Cheese()  I can think of only one way to do this, but this seems clunky: class Cheese():     def __init__(self, num_holes = 0):         if (num_holes == 0):             # Randomize number_of_holes         else:             number_of_holes = num_holes  What do you say? Is there another way? is it possible to display a Google Earth map INSIDE Excel? Is there any way, using the scripting available to Excel 2007 to display a Google Earth map inside a sheet?  I've used Excel to house the data that I've then gone and generated a KML file to load into Google Earth, but now they want to see a pretty little cell with a client address mapped out in Excel directly to pretty up the presentation. Current sensing nA to mA I need to sense the current of a target  through various periods of its on/sleep/off state and then need to send this data back to another interface MCU to read out the value. They will be both on the same board, powered by 5&nbsp;V USB.  However these are the requirements I have:   5&nbsp;V USB PSU Must be able to sense currents in the range of nA to mA with high    accuracy/precision. (I figure 1&nbsp;nA to 500&nbsp;mA) Only measure the current of the target MCU and not the interface. Must output maximum 3.3&nbsp;V interface MCU   I have looked at available options and current sense amplifiers by Texas Instruments can't sense nA due to higher bias currents. So therefore I feel I would need a precision amplifier.  However I am stuck on how to proceed with this because, I need to somehow have a automatic dynamic current range and I am fairly new to current sensing and am not really sure on all the specifics. Is there evidence that adding salt to water prior to boiling can damage a stainless steel pan? How to remove uninstalled wine app icons from unity dash? I installed  (for Windows) using wine but turns out LAN Messenger is also available for linux as well. So..   I uninstalled LAN Messenger from wine. I also removed wine. deleted the .wine directory. after that sudo apt-get autoremove and sudo apt-get autoclean. then I installed LAN Messenger using dpkg -i pkgname.deb and it installed successfully.   The problem is that now I get this in dash:   Any Help is highly appreciated.  [NOTE] I am using ubuntu 12.10 Thermistor control of peltier voltage with Arduino (for DSLR chill box project) I am mildly familiar with electronics, mostly from playing around with electronics kits as a kid. That was a long time ago, though, maybe as much as 20 years ago. I am currently working on a cold or "chill" box for my Canon 5D III, so I can keep it's temperature very low, and very consistent, for doing low noise astrophotography.  I have a general design for the box, and I'm using a single 12v 5.8amp peltier (TEC) attached directly to a copper box for cooling. The box is currently insulated with extruded foam board, and the hot plate of the peltier will be cooled with a water cooler from an old computer kit.   I'm getting more ambitious with my project, however. I want thermal regulation, to maintain a consistent temperature, and I'd eventually like to get into two-stage cooling to achieve a Delta-T of closer to -55-60°C relative to ambient (the chill box will be cooling the camera, so the sensor will be warmer, probably by as much as 10°C, than the temperature of the copper plating in the box itself.) I want to have two primary modes:   Rapid cooling mode, operating the peltier at 12v or higher (max voltage is 15.4v) to quickly cool the box down to the target temperature. Regulated maintenance mode, operating the peltier at lower voltages to maintain a consistent temperature, above the maximum potential cooling the peltier can supply (for headroom as the voltage is adjusted in response to small temperature fluctuations).   I'd like to maintain temperature within 2-3°C if possible. I've looked into Arduino (and I've messed with similar things in the past), and it seems perfectly ideal for the task, with one exception: It doesn't seem to handle the kind of current I need top power a single peltier, and certainly not two.   I've done some research on how I might achieve this, but I'm falling up short on my understanding of the electronics involved. I've found a two-relay "shield" for Arduino Uno that can power two devices with up to 8amps each, and up to 30v each. That can be controlled from the Arduino itself. It seems the design of a relay uses a magnetic coil to actuate a switch that allows an independent power source to be used to power components like a motor, solenoid, or in my case a peltier. I haven't found any way of actually regulating the voltage of the relay with the Arduino, however.  So I kept investigating, and I came across some schematics that showed how to use transistors, specific mosfets to be exact, where the base was connected to an Arduino output, and the collector/emitter were connected to the power loop of whatever needed to be powered at a higher voltage (not sure about current here), and this still allowed control of the voltage.   It's been so long since I messed with any of these components, my memory is extremely rough, and I'm not quite connecting how it all works. I'd be happy with some references to complete examples of powering, and controlling the voltage of, high powered devices via an Arduino, but if anyone here can explain how all this works and why, that would be most ideal. I'd rather understand the concepts, so I can reapply them later, than just have a pattern to follow. Dollar cost averaging - Should I still do it if I have a large pile of cash now? I currently have a large pile of cash savings ($240,000) which I really should have been investing all this time, but the past is past and no point dwelling on it.  I am currently 38 years old (2 kids. Wife who is also a high earner - $100,000), with a high salary ($150,000). I have read "The Intelligent Investor" and am really sold on dollar cost averaging as a strategy, using the index funds offered by Vanguard.  My current dilemma is what to do with the cash I already have. My current plan is to still follow the dollar cost averaging and slowly move it into vanguard over a period of 4 years (~$5000 per month). While leaving the remaining parts of the cash in term deposits. So $50,000 in a 3 year term deposit at 3%, $50,000 in a 2 year term deposit at 2.8% etc.  But in someways it feels overly conservative. Should I just move all the money now? Or perhaps in a shorter time frame (3 years? 2 years? 1 year?).  There are a few other questions on the site similar to mine, but they are from 2013/2014 etc. Given that currently the stock market is at a high and there is a lot of economic uncertainty on the horizon, putting everything in the stock/bond market at once now seems like a risky move. And it seems to violate the principle of dollar cost averaging. Or am I violating dollar cost averaging by trying to "time the market" by looking at it's current value?  Reading this section  seems to indicate that I should just invest everything now. But the first paragraph also seems to suggest giving more weight to that advice if the market was trending upwards (Which I am not certain the current market is/will be for long).  PS: My current investment horizon is long. Basically retirement, about 20 years from now. How can I make a rounded indentation on a cylinder? I'm trying to do a cosmetic bottle in blender but i don't how to do this thing in the image. How to do this round edge on the cap. Can anyone help me? When editing a question on , I observed that a link which was not rendered in the post was hyperlinked in the edit preview (see pictures below). I tried reproducing it in the  to see if this also happens when the post is posted for the first time and observed the same. It seems to be a bug after the shift to CommonMark, leading to the different rendering of links on client and server-side. A link following a special character (without any space) is not hyperlinked in the post but is hyperlinked in the preview. A link separated from the special character with a white space appears to have no such problem. (see pictures below and my ). Link not hyperlinked in post  Same link hyperlinked in preview I have:  &lt;?php  $file=fopen(date("Y-m-d").".txt","r+") or exit("Unable to open file!");  if ($_POST["lastname"] &lt;&gt; "") {    fwrite($file,$_POST["lastname"]."\n"); }  fclose($file);  ?&gt;   but it overwrites the beginning of the file.  How do I make it insert? I received a mail today from Academia.edu (a site I wasn't previously aware of), asking me to confirm that I co-authored a paper with a colleague.  Having looked into it a little it sounds like it might be a useful site - the idea of a "social network for scientists" is one I've seen the need for in the past. However, partly due to bad experiences with the seemingly similar ResearchGate, I'm also skeptical.* Without signing up for an academia.edu account the site doesn't offer much information, so I would like the following information:   What specific features does academia.edu offer to its users? Is it genuinely useful for any of the following purposes (each of which seems genuinely needed)   as a platform for networking with academics for discovering relevant research as an effective system for post-publication peer review for organising references among a small team of people working on a project  Will it send out mails to my colleagues without my express and explicit permission? (I.e. are the mails I received today the result of a deliberate action by my colleague, who is aware that I will be emailed and wishes me to join the site; or are they essentially spam from a social networking site aggressively trying to expand its user base?) It's clear from its  that it's a private, venture-capital funded company. What is its business model?   In short, is this a site that has some genuine utility for academics, or should I just ignore it?  *I've never signed up for ResearchGate but I regularly receive spam from it purporting to be from my colleagues, who aren't aware that it's being sent on their behalf. I would be mortified if my senior colleagues received such mails claiming to be from me, so I won't touch it with a barge pole. Assigning values to divergent series I have been looking at divergent series on wikipedia and other sources and it seems people give finite "values" to specific ones. I understand that these values sometimes reflect the algebraic properties of the series in question, but do not actually represent what the series converges to, which is infinity. Why is it usefull to assign values to divergent series?  The only theory I could come up with, is this:  Say you have 2 divergent series, series' A and B, and you assign each a value,   Series ($A= \sum_{n=0}^\infty a_n$), which I assigned the value Q  and series ($B= \sum_{n=0}^\infty b_n$ ), which I assigned the value P  But it just so happens that series $C=A-B= \sum_{n=0}^\infty (a_n-b_n)$ converges. Could that imply that the actual value of series $C$ is the difference of the two assigned values to $A$ and $B$, that is $\sum_{n=0}^\infty (a_n-b_n)=Q-P$ ?  If so, then that would make some sense to me, as to why people sometimes assign values to divergent series.