I'm working on a proof that $$\gcd(Fn, Fn-1) = 1$$ for all n greater than or equal to 0. Here's what I have so far. I used a proof by induction. I used $$\gcd(1,0) = 1 $$ for the base case. For the inductive step I assumed $$\gcd(F_n, F_{n-1}) = 1$$ and set up $$\gcd(F_{n+1}, F_n)$$ $$ = \gcd(F_n, F_{n+1} \bmod Fn)$$ $$ = \gcd(F_n, (F_n + F_{n-1]) \bmod Fn)$$ I'm a bit confused about what to do at this step. Do I use $$\gcd(a+b, b) = \gcd(a,b)$$? If so, how do I prove that? Would appreciate some help!

I have a bit difficulty to proofe that two consecutive numbers are coprime. I have the following  The property $P(n)$ is the equation $(F_{n+1},F_n)=1$ where F_i the sequence of fibonacci is and $n \in \mathbb {N}$.  Induction hypothesis: $gcd(F_{n+1},F_n)=1$  $P(0)$ is true because $F_1=1, F_0=1$ and $gcd(1,1)=1$  To show: $gcd(F_{n+2},F_{n+1})=1$  Proof:  Fibonacci formula says  $F_{n+2}=F_{n+1}+F_n$  This is as faar as I got. How can I now get to $gcd(F_{n+2},F_{n+1})=gcd(F_{n+1},F_n)$ which would then proofe it?


I have a string whose value is '12345678'. I want to assign this value to integer array like the first index of the array contains 1, the second index of array contains 2 so on. So when I write below code and execute then i received value 48 for 0 index and  value 49 for second index, ascii value of my number.  Declaration   int[] ArryDIReadValue = new int[DI_COUNT_CHANNEL]; string binary = Convert.ToString(portData, 2);  ArryDIReadValue = binary.Select(n => Convert.ToInt32(n)).ToArray();   Could someone please help to overcome this problem.

I have a char in c#:  char foo = '2';   Now I want to get the 2 into an int.  I find that Convert.ToInt32 returns the actual decimal value of the char and not the number 2.  The following will work:  int bar = Convert.ToInt32(new string(foo, 1));   int.parse only works on strings as well.    Is there no native function in C# to go from a char to int without making it a string?  I know this is trivial but it just seems odd that there's nothing native to directly make the conversion.


I am Canadian Permanent Resident with an Indian passport.I have a multi entry UK business visa which is for valid for 2 years but I have not used to enter to UK as of now.I am planning to travel from Canada to India on a personal visit.My wife who is also a permanent resident and indian passport holder plus my daughter who is also a permanent resident of canada with indian passport are travelling with me.We have flight from Halifax to London and the connecting flight from London to Delhi.The London to delhi flight is after 16 hours .The date of landing in london is Dec 1st while ongoing journey flight to india is on next calendar day.My question is that would we all require UK visa  for transit or since I do have business visa,I do not require visa.Also my son who is a canadian passport is travelling with us.I understand for him we do not need visa.

Is there a website or some other way to find out if I need a transit visa for a short stop in the UK on my way somewhere else? Ideally this should give me the answer for all nationalities, and take into account any other visas I may have.


Overall code coverage set from salesforce is 75% we can cover upto 100% but why they set for 75% only not set 100%.

This might be a silly question, but I am new to Salesforce, so I am asking this question that why there is 75% code coverage concept is there in salesforce?  What I know, in order to deploy or create a package 75% code coverage is mandetory.  But why this percenatge concept is a very improtant aspect in salesforce.  Regards


I am dealing with a question in Stewart Calculus Book which states the following: Using Lagrange multiplier, find the maximum of the function $$f(x_1,x_2,...,x_n)=(x_1x_2...x_n)^{1/n}$$subject to the constraint$$\sum_{i=1}^{n} x_i=c$$,where $x_i$'s are all positive, and use this to prove the AM-GM inequality. Actually in AM-GM inequality, it holds for all nonnegative numbers, but I think the author wants to get rid of the case where $x_i$'s are all zero, where Lagrange multiplier can no longer be applied. And the result I obtained is: $f$ will have its maximum/minimum (the arithmetic mean), or even saddle point at $(\frac{c}{n},\frac{c}{n},...,\frac{c}{n})$, since Lagrange method gives no definiteness on the behaviour of the critical points found (whether max, min, or saddle). And my question is: In this case, how do we show that the point I found gives the maximum value of the function? My teacher gave me an argument that said "the minimum value would be some place very near to $0$, so the arithmetic mean will not be the minimum value". But I think the argument is not persuasive enough to explain why the arithmetic mean is the maximum value. So, I hope that there will someone who are willing to give their opinions on this. Thanks.

Exercise: Let $x_1,x_2,...,x_n$ be real positive numbers. Prove the arithmetic-geometric mean inequality, $(x_1x_2...x_n)^{1/n}\le (x_1+x_2+...+x_n)/n$.  Hint: Consider the function $f(x_1,x_2,...,x_n)=(x_1+x_2+...+x_n)/n$ subject to the constraint $x_1x_2...x_n=c$ a constant.  My work:  Consider $f(x_1,x_2,...x_n)=(x_1+x_2+...+x_n)/n$ on $S=\{(x_1,x_2,...,x_n) | x_1x_2...x_n=c\}$  $g(x_1,x_2,...,x_n)=x_1x_2...x_n-c=0$  $\nabla f(x_1,x_2,...,x_n)=(1/n,1/n...,1/n)$  $\nabla g(x_1,x_2,...,x_n)=(c/x_1,c/x_2,...c/x_n)$  $\nabla f = \lambda \nabla g$  $1/(n\lambda)=c/x_1=c/x_2=...=c/x_n$  $x_1=x_2=...=x_n=n\lambda c$  At the point $(n\lambda c, n\lambda c,... n\lambda c)$, $f$ on $S$ takes either a maximum or a minimum.  $f(n\lambda c, n\lambda c,...,n\lambda c)=n(n\lambda c)/n=n\lambda c$  $(n\lambda c*n\lambda c*...*n\lambda c)^{1/n}=((n\lambda c)^n)^{1/n}=n\lambda c = f(n\lambda c, n\lambda c,...,n\lambda c)$  This shows the equality case. To prove the inequality, I want to show that at the point $(n\lambda c,n\lambda c,...,n\lambda c)$, $f$ on $S$ takes a maximum minimum. I tried proving that the Hessian is negative positive definite, but I had trouble working with the second derivatives. I've looked up various proofs for the AM-GM inequality. The Lagrange ones didn't make full sense to me, so I thought I would turn to MSE. Any ideas? Thanks!


If part of the party enters combat with enemies but the rest of the party is not aware of the threat or aware there is combat happening yet, does a player with the Alert feat who rolls highest on initiative act before even the enemies? In this example, the Archer has the Alert feat but is hanging back behind a corner waiting for the Paladin to see if things are safe. The group rolls Initiative and the Archer rolls 21, the Spiders roll 15, and the Paladin rolls 8. The Spiders roll 24 for Stealth and Surprise the Paladin. Who acts first? The only answers I come up with seem to unfairly negate the Archer's choice to take the Alert feat.  The relevant part of the Alert feat:  You can't be surprised while you are conscious.

My character was unaware of a group of bandits, but  my character cannot be surprised (I have a Weapon of warning) but the rest of my group is out of the range of my weapon of warning, do I get to take my turn even when the rest of my party was surprised? Do I take my turn before the attack of the enemy if my initiative is   high enough? Please help.


This is how it looks. I wonder if it's possible to merge the 2 unallocated partitions without data loss

I am currently dualbooted between Windows 8 and Linux Mint 18  Using GParted, I see this following:   The selection partition is unallocated for a size of 25 GB, I would like to merge this with my dev/sda6 (linux partition), so that I can make my linux partition about 50GB. I'm not really sure about the process though on how to do this? I try to resize dev/sda6, but I see that the maximum size and minimum size are the same. How do I merge the unaccolated space?


I'm an English major and planning to apply to graduate schools. My freshman year I originally planned to be a bio major due to pressures from my family. I had to take chemistry and biology, which soon enough turned into a disaster. I dropped chem, but since I needed enough credits to be considered full time, I was forced to keep with bio. I ended up with a D- in the course. If it wasn't my freshman year, I honestly would have probably done better, but I was having a rough time settling into college with homesickness and depression. Aside from that one hiccup, however, the rest of my grades are As with a couple B+. So what I'm wondering is would that badly affect my application or even receiving scholarships?

I'm currently an M. Phil student in Math and I failed a course last semester because I was not able to hand in a home work assignment (which was worth 40% of my grade) on time (I was 30 minutes late).   Apart from that I'd say I'm a fairly decent student, I got an upper second class honours bachelors degree, I have a B+ and A's for all my other courses in my current programme and I'm almost finished with my first paper to be published.   I've however been deeply worried about this failure as it would reflect poorly on my transcript if I were to apply to a Ph.D or another Master's programme.   Will my failing grade affect my chances of getting into a competitive programme or greatly lower my chances of getting a scholarship?


How would I come to a general form of this type of summation, similar to   $$\sum_{i=1}^n i = \frac{n(n+1)}{2}$$ and  $$\sum_{i=1}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ ?  I found this post about calculating higher powers of i, but am unsure if this would apply for negative powers as well: , as his formula:  $$\sum_{n=0}^N n^{m+1} = \frac{N^{m+2}}{m+2}+N^{m+1}$$ results in dividing by 0 (zero) for m = -2.  Also, How could I extrapolate for the more general form  $$\sum_{i=1}^n \frac{1}{i^k}$$ where k is some constant? This is my first StackExchange post, so feel free to give me tips on how to improve my posts. Thank you.   Edit: I have now learned that there is no rational closed form expression of the Harmonic numbers, But can someone explain why, or simplify another proof explaining why?

One of the joys of high-school mathematics is summing a complicated series to get a “closed-form” expression. And of course many of us have tried summing the harmonic series $H_n =\sum \limits_{k \leq n} \frac{1}{k}$, and failed. But should we necessarily fail?      More precisely, is it known that $H_n$ cannot be written in terms of the elementary functions, say, the rational functions, $\exp(x)$ and $\ln x$? If so, how is such a theorem proved?    Note. When I started writing the question, I was going to ask if it is known that the harmonic function cannot be represented simply as a rational function? But this is easy to see, since $H_n$ grows like $\ln n+O(1)$, whereas no rational function grows logarithmically.  Added note: This  asks a similar question for “elementary integration”. I guess I am asking if there is an analogous theory of “elementary summation”.


I want to show that if $x$ is rational and nonzero then $e^x$ is irrational.  Clearly $e^{\frac{r}{s}} = \frac{p}{q} \Rightarrow q^s e^r = p^s$, but this doesn't seem helpful. The usual proof that $e$ is irrational doesn't look like it can be extended either.

Let $n$ be a positive integer. I know the traditional proof that $e$ is irrational. How do we show that $e^n$ is irrational in some sort of similar line? I am of course assuming it is but I would be astounded if not. It occurs to me that since $e$ is transcendental, of course $e^n$ is irrational, but I don't want to use that fact.  Googling gives me something for $e^2$, but I could not easily find anything for $e^3$.


I am doing my homework but I find it has problem here:   public static void test(int[] a){      for(int i = 0; i < a.length;i++){         a[i] = i;     } }  public static void main(String[] args) {     // TODO Auto-generated method stub      int [] ints = {1,1,3,3,1,1,2,2,34,4,5,56};     test(ints);     for(int i = 0; i < ints.length;i++){         System.out.print(ints[i] + " ");     } }   In this case, system will print out: 0 1 2 3 4 5 6 7 8 9 10 11  But When I change the test method to  public static void test(int[] a){         int [] a2 = {2,2,2,2,2,1,2,2,34,4,5,56};         a = a2;  }   main method system will print: 1 1 3 3 1 1 2 2 34 4 5 56     which seems like this array are not changed. Why this happen? I know maybe this is something called pass by value or reference. But I am still confusing about it.

I always thought Java uses pass-by-reference. However, I've seen a couple of blog posts (for example, ) that claim that it isn't (the blog post says that Java uses pass-by-value). I don't think I understand the distinction they're making. What is the explanation?


I am trying to replicate a method to cook lamb I experienced in a North African restaurant in Paris. The dish was called "mechoui" (which is a whole-hog ... hmm... lamb outdoor roasting tradition), but when I asked the chef he said all he did was cook the lamb pieces at 300F (180C) for 1hr in the oven with no fat, just some coarse salt. The lamb (typically a sub section of lamb shoulder with some bone) was served just about fall of the bone tender, with plenty of delicious browned bits. It was clearly roasted and not braised. Each time I have tried to replicate this I end up with a messy & disappointing situation: plenty of liquid released in the pan, no browning, and tough meat. What would people recommend?

All,  I would like to cook spare ribs to a fall-off-the-bone consistency.  I don't have access to a grill.  I know how to do that with pork shoulders (dry rubbed, then uncovered in the oven at low heat for 6-8hrs), but spare ribs are a different type of animal.  They are individually smaller pieces (my ribs are sawed in chunks), and they are fairly fatty, with a big bone.  What should I do?  Should I pan-sear them first, do I need some liquid in the dish?  Should I cover them?  Thanks,  JDelage


Let $X_1$ and $X_2$ be real-valued independent random variables with a standard normal distribution. Let $ Y = X_1X_2$. Find the characteristic function of Y.  Attempt:  $\phi_{Y}(t)$ = $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty} exp(it(x_1x_2))exp(-1/2(x_1x_2)^2)dx_1dx_2$  I know that the standard normal characteristic function is:  $\phi_{X_1}(t)$ = $exp(\frac{-t^2}{2})$ and likewise for $X_2$  However, I'm not sure what the resulting product is. I realize that I can use a Jacobian, but I'd like to keep it simple and see if there is a way to derive the characteristic function with something easier.

Can anybody please suggest how I can compute the moment generating function of the inner product of two Gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each other? Is there some standard result available for this? Any pointer is highly appreciated.


What are the effects and implications of choosing one of the following two options over the other?   Performance differences? Stability differences? Which of the two is better supported long-term?

After upgrading to 15.04, I have one additional driver (it did not appear in 14.10). What is the purpose of this driver and should I enable it?


A rose of the form $r = \cos(c\theta)$ normally has $2c$ petals when $c$ is even and $c$ petals when $c$ is odd. A rose may also have $4c$ petals when $c$ can be expressed as $Z + \frac{1}{2}$ where $Z$ is an integer. A rose may also have $12c$ petals when $c$ can be expressed as $Z \pm \frac{1}{6}$.  A rose may also have as many petals as one with $3c$ when $c$ can be expressed as $\frac{Q}{3}$ but not as $Z$ where $Q$ is either $Z$ or $\frac{Q}{3}$. How is a rose with 30 petals graphed (in the form shown above)?

In polar coordinates $(r, \theta)$, the equation $$r = \sin\left(a \theta\right)$$ gives a rose with $a$ petals if $a$ is odd, or $2a$ petals if $a$ is even.  Thus, the number of petals generated for some values of $a$ are     a   | petals =======+========    1   |   1    2   |   4    3   |   3    4   |   8    5   |   5    6   |   12    7   |   7   Conspicuously missing from this table are roses with $4n+2$ petals. How can you generate a rose of the same "shape" with $2, 6, 10, \ldots$ petals? If you can't, why (intuitively) is it impossible?


I noticed that in mysql i can't make an except on selecting some columns, there is my request:  SELECT * FROM plane as p JOIN type as t ON p.id=t.id;  But this shows me all columns even the two columns plane_id and type_id that are equivalent, is there a request i can do to print just one of them and excepting the other ??

I'm trying to use a select statement to get all of the columns from a certain MySQL table except one. Is there a simple way to do this?  EDIT: There are 53 columns in this table (NOT MY DESIGN)


I have a simple question.  I'm looking at using  for my project and I need to be able to draw ~500ma from the 'Q' or '!Q' pin on the flipflop.  How much current can I draw?  I looked at the datasheet and couldn't find that information.

I'm attempting to make an EEPROM burning circuit using an Arduino Uno. Due to the lack of pins on the Uno, I opted to use shift registers for the address and data pins of this EEPROM. Aside from my current issue, everything will be powered from the 5v pin.  Before I ask my question, I'd like to clarify that I am an electronics beginner. Sure, I could have purchased an EPROM burner for ~$100 USD for this chip, but I'm a very DIY kind of guy and I only have a couple of these to burn, so the price doesn't seem to justify the cost.  The issue I'm examining now, before plugging in my circuit is I can't seem to find the maximum current allowed through a Q pin on this dual flip flop (). I want to ensure I won't release the magic smoke from this IC by simply plugging it in. The purpose of this flip flop (as of now) is to toggle between read and write states for the EEPROM. As such, I've wired the VCC pins of an  and  to Q and !Q (unsure how to notate that here on SE) such that if one is on the other is off, and vice versa.  The CD4013B is running at only 5V, that's power and all inputs.  Here is what I think I know, and please correct me if I'm wrong!  (I mean, I bought extras just in case, but still...)   The SN74HC595 should not draw (or be loaded) over 35mA, or more likely 30 for a safety margin. The SN74HC165 should not draw (or be loaded) over 25mA / 20 or so for safety.   Now, being as these are both being used as for EEPROM data pins, I can imagine that the actual power draw will be significantly less than those maximums (though by how much I am really unsure).  Looking at the CD4013B datasheet, I can't seem to find any information regarding how much current this chip can handle.  Also, while I'm here talking about this specific IC, I'm finding the datasheet somewhat confusing.   The output high current is always listed as a negative amperage... I didn't even realize this was possible. Is it due to the transistor logic of this particular device that current flows (I would assume) backwards?  I also find it strange that the pins on this device are Vdd and Vss rather than Vcc and ground. Anybody care to explain why this is?


If current is passed through an inductor, there will be a voltage across it. If that current source is disconnected, the voltage across it reverses. Does this happen instantly?

I understand that inductor current and capacitor voltage cannot change abruptly, but can inductor voltage and capacitor current change abruptly?  I have a feeling the answer is no but I cannot explain why.


A set $E \subseteq \mathbb{R}$ is measurable if for any subset $A\subset\mathbb{R}$,  $$\mu(A)=\mu(A\cap E)+\mu(A\cap E^c).$$ where $\mu$ is the Lebesgue outer measure.  A function $\varphi : \mathbb{R} \to \mathbb{R}$ is measurable if for any $\alpha\in\mathbb{R}$ the set $E_\alpha:=\{x\in\mathbb{R} : \varphi(x)>\alpha\}$ is measurable.  Let $\varphi : \mathbb{R} \to \mathbb{R}$ be a measurable function, and let $\ \ f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous function.   For two such functions we know that the composite fonction $f\circ\varphi$ is measurable because of a result that say $\varphi^{-1}(A)$ is measurable for any borelian set $A$ (our borelian here is $f^{-1}(]\alpha,\infty[)$).  Now I would like to know why for two functions $\ f$ and $\varphi$ like above $\varphi\circ f$ is not necessarily a measurable function.   Edit: The first answer of  gives an example of such a pair of functions.

We know that if $ f: E \to \mathbb{R} $ is a Lebesgue-measurable function and $ g: \mathbb{R} \to \mathbb{R} $ is a continuous function, then $ g \circ f $ is Lebesgue-measurable. Can one replace the continuous function $ g $ by a Lebesgue-measurable function without affecting the validity of the previous result?


Prove that $$2\times 2! + 3\times 3!+4\times 4! +....+n\times n!=(n+1)!-2$$ I know that it can be proved by mathematical induction, but I want to prove it without using the mathematical induction. I tied the equation $$C^n_0 + C^n_1 + C^n_2 +...+C^n_n=2^n$$ But I did not get any thing useful.

$$\sum_{k=1}^nk(k!)$$  I know the answer is (n+1)!-1..I can solve this question using principle of mathematical induction...but I would like to know if there is any other alternative approach


I recently wrote my very first trigger and I'm looking to deploy to production. Before deploying I need help with writing test code but I don't know what I'm doing. Basically i want to test my trigger but I don't know how to write test cold.  the goal is to enter a date in the opportunity object field titled: Initial Field Visit Completed.  I have copied the trigger below and if you guys can provide suggestions that would be greatly appreciated.  trigger FieldVisitCompleted on Opportunity (after insert,after update) { Set <Id> oppIds = new Set<Id>();  List<Lead_Source__c> ls= new List<Lead_Source__c>();      for (Opportunity parentObj : Trigger.new)     {       oppIds.add(parentObj.Id);     }      Map<Id, Lead_Source__c> parentObjList = new Map<Id, Lead_Source__c>([Select Id,Effort__c,Initial_Field_Visit__c FROM Lead_Source__c WHERE Effort__c IN :oppIds]);             for (Lead_Source__c lsrc : parentObjList.values()) {                    System.debug('lead source'+lsrc);                    Opportunity opp = Trigger.newMap.get(lsrc.Effort__c);                    Opportunity o = Trigger.oldMap.get(lsrc.Effort__c);                    System.debug('opp field'+opp.Initial_Field_Visit_Completed__c);                    System.debug('opp field'+ o.Initial_Field_Visit_Completed__c);                 if(opp.Initial_Field_Visit_Completed__c != o.Initial_Field_Visit_Completed__c){                     lsrc.Initial_Field_Visit__c = opp.Initial_Field_Visit_Completed__c;                    System.debug('lsrc field'+lsrc.Initial_Field_Visit__c);                    ls.add(lsrc);                 }              }       if(!ls.isEmpty()){          update ls;      } }   Here is what I have so far for test code  @isTest  public class FieldVisitTestClass {        static testMethod void myTest() {           Opportunity opp = new Opportunity();           opp.name = 'Michael Jordan';           opp.AccountId = opp.Id;       } }   Looking for some direction as to where to go from here.

How do I write a unit-test / test class for a trigger?  What are my options?   Inline with the trigger?  New Class?


If I start with an  on the battlefield and cast , how much health would I gain? I know it is somewhere between 4 and 6.  Posible options in my mind: a. The tokens enter at the same time, but the rally ability only counts there being two creatures on at once: The Ondu Cleric, and the token who activated Ondu Cleric's ability. This happens twice, so 2*2 is 4. (Didn't seem likely, but hey, this might be the case) b. The tokens enter one at a time, and the rally ability gives 2 health, then 3 health for a total of 5. c. The tokens enter at the same time, and the rally ability counts 3 creatures both times it is activated for a total of 6 (2*3).  Optional Question: What if I started with 2 Ondu Clerics on the battlefield? Would that just double the health gained, or would something else happen?

I was playing modern with the owner of a shop.  He played a  which he used to bring in 7 lands: 5 basic mountains and 2  cards.  He then claimed that each  triggered 5 times (killing me).  I am doubting this now.    Here is my reason: The two  cards entered at the same time as the other 5 basic lands.  That means when they were on the battlefield and their ability was in effect, the other 5 basic lands were already there too.  That seems too late to trigger a "Enters the Battlefield" effect.  So here is my question.  Am I right or wrong?  If I am wrong, please show me how the enter the battlefield effect can trigger for something that enters the battlefield at the same time as itself.  If I am right, please show me the rules that prove it.  I now have two shop owners that are convinced that this is a legal play.  If it is not legal, I am going to need clear rules citations to convince them.    Side note:  If I am wrong and it is a legal play, then I have a follow up scenario.  Say I have 2  cards and 5 other human cards in my graveyard.  If I play a spell that lets me return all of them to the battlefield at the same time (say ), would the  cards get 6 +1/+1 counters on them?    To me, if the trick that was played on me with  is legal then my  cards should also get the +1/+1 counters.


The rate of expansion of the universe is   The age of the universe is   That places the furthest theoretically observable edge of universe at 13.798 bln light years away - this is how long light would take to reach us from there, and there were no light sources before that date.  Now, how fast does the observable part of the universe expand? A bit of unit conversion and multiplication:  13798000000 light years in megaparsecs = 4 230.39567 megaParsecs   74.2km/sec in light years/year = 0.000247504559 light years / year   Multiply the two, and I get the expansion rate:  1.04704221 light years per year per distance to the observable edge of the universe.  Speed of 1 light year per year is the speed of light. The 0.047 seems awfully small.  Probably within error margin of the universe expansion speed and age of the universe estimates.   Is this a coincidence, or is this somehow bound - and if so, what are the consequences?

The Hubble time is about 14 billion years. The estimated current age of the Universe is about 13.7 billion years. Is the reason these two time are so close (a) a coincidence, or (b) a reflection that for much of its history the Universe has been expanding at a constant rate?


Obviously my own mail servers should be marked as "allow" in an SPF record, but I'm not so sure about mail relays (e.g. my ISP). Since other people (not related at all with my server) also send email through the same relay, it seems to me the most appropriate choice would be listing the relays as "neutral" like:   v=spf1 ip4:myserverip ?include:_spf.myisp.com -all   Is this common practice? Or is there some better option?

This is a  about setting up .     I have an office with many computers that share a single external ip (I'm unsure if the address is static or dynamic). Each computer connects to our mail server via IMAP using outlook. Email is sent and received by those computers, and some users send and receive email on their mobile phones as well.  I am using  to generate an SPF record and I'm unsure about some of the fields in the wizard, specifically:   Enter any other domains who may send or relay mail for this domain Enter any IP addresses in CIDR format for netblocks that originate or relay mail for this domain Enter any other hosts which can send or relay mail for this domain How stringent should SPF-aware MTA's treat this?   the first few questions i'm fairly certain about... hope i have given enough info.


I am confuse on the how exactly rotational matrices work. So I understand that you can rotate a point around the x, y and z axis but if asked how you find a single matrix that will show the same rotation if you were to rotate it along the x, y and z axis in that order. Any help would be appreciated!

Given are now two matrices and I have to discuss what the given functions are doing (geometrically). Maybe you can revise/add the following:  given are the matrices  $ A = \begin{pmatrix} \cos(a) & -\sin(a) & 0 \\ \sin(a) & \cos(b) & 0 \\ 0 & 0 & 1 \end{pmatrix}$  $ B = \begin{pmatrix} \cos(b) & 0 & -\sin(b) \\ 0 & 1 & 0 \\ \sin(b) & 0 & \cos(b) \end{pmatrix}$.  (1) What does $f: \mathbb{R^3} \to \mathbb{R^3}, x \to Ax$ mean?  It means a rotation around the z-axis.   I do $A*(1,0,0) = (\cos(a), \sin(a), 0)$. This is a rotation around z-axis counterclockwise.  I do $A*(0,1,1) = (-\sin(a), \cos(a), 0)$. This is a rotation around z-axis counterclockwise.  I do $A*(0,0,1) = (0,0,1)$. It remains.  (2) What does $g: \mathbb{R^3} \to \mathbb{R^3}, x \to Bx$ mean?  It means a rotation around y-axis.  I do $B*(1,0,0) = (\cos(b), 0, \sin(b))$. This is a rotation around y-axis clockwise.  I do $B*(0,1,0) = (0, 1, 0)$. It remains.  I do $B*(0,0,1) = (-\sin(b), 0, \cos(b))$. This is a rotation around y-axis clockwise.  (3) What does $h: \mathbb{R^3} \to \mathbb{R^3}, x \to ABx$ mean?  I do A*B and then  I do $AB*(1,0,0) = \begin{pmatrix} \cos(a)cos(b) \\ \sin(a)\cos(b) \\ \sin(b) \end{pmatrix}$. This is.. ?!  I do $AB*(0,1,0) = \begin{pmatrix} -\sin(a) \\ \cos(a) \\ 0 \end{pmatrix}$. So this should be again a rotation around z-axis for (a). Regardless of what degree b is!  I do $AB*(0,0,1) = \begin{pmatrix} -\cos(a)\sin(b) \\ -\sin(a)\sin(b) \\ \cos(b) \end{pmatrix}$. ?!  And so on.


Mei Terumi, the 5th Mizukage is always angry and tensed at the thought of marriage.  Who does she marry anyway? Does Chojuro get her?

In the last chapter of Naruto, some characters got married, and some of them had kids. What is the entire husband-wife-kids set?


I am trying to rank in the SERP's for the query "t-slot aluminum" or "t slot aluminum". I was beginning to see some progress and peaked at a position of 15.2 on August 11. Since that date, my ranking has incrementally reduced. I saw the biggest drop on August 15.   I have done nothing significant to reduce this ranking. The only thing I changed was adding/removing a Facebook pixel. Over the last three weeks the pixel is no longer in the page's file.  Does anyone see what could potentially be wrong? I have no errors in Search Console.  Update:  This has actually happened to several queries for my site. I was looking on SEMrush today and saw there was a Google change seven days ago. This is where the majority of my page ranks dropped.   The message shows that it has to do with page reviews. My site does not have any product/service reviews because it is not applicable.  Why would this affect me so much?

There has been a significant drop (90%) in traffic from Google to one of my well-established sites (6+ years) in the last week. Searches show that the top 3 wide keywords all dropped 4 spots. Searches for other keywords do not show ANY results in the first 10 to 25 pages of results, while previously one 1st or 2nd page at most.  Since there are , the question really is:  What steps are necessary to figure out what caused such a drop?  There have been no major changes during this period or the last month on the site and certainly not in the homepage which has dropped in rank. Over all the years of running this site and plenty of others, I have never experienced this. There are is duplicate content on my site and I have rigorously used canonical links for the last few years to ensure it is not misinterpreted as such.


After installing Ubuntu 20.04 I removed snapd and want to use good old apt, but when I type:  sudo apt install chromium-browser   I get this:  The following additional packages will be installed: snapd The following NEW packages will be installed: chromium-browser snapd   Which installed:   snapd  and then use snapd to install chromium.    I understand that Chromium team go with snap-only approach (, which is bad, but it's their choice), but I added chromium ppa which won't work for Ubuntu 20.04.   Can I disable snap-only installation for apt?  I faced several issuses with snap, eg. the current version of Chromium from snap can't open xdg-open links, while apt version on Ubuntu 18.04 can.

When I do  apt-get install chromium-browser   it downloads some .deb file, and then installs a snap package:  Selecting previously unselected package chromium-browser. (Reading database ... 227048 files and directories currently installed.) Preparing to unpack .../chromium-browser_77.0.3865.120-0ubuntu1~snap1_amd64.deb ... => Installing the chromium snap ==> Checking connectivity with the snap store ==> Installing the chromium snap Warning: /snap/bin was not found in your $PATH. If you've not restarted your          session since you installed snapd, try doing that. Please see          https://forum.snapcraft.io/t/9469 for more details.  chromium 78.0.3904.70 from Canonical✓ installed => Snap installation complete Unpacking chromium-browser (77.0.3865.120-0ubuntu1~snap1) ... Setting up chromium-browser (77.0.3865.120-0ubuntu1~snap1) ... Processing triggers for mime-support (3.63ubuntu1) ... Processing triggers for hicolor-icon-theme (0.17-2) ... Processing triggers for gnome-menus (3.32.0-1ubuntu1) ... Processing triggers for desktop-file-utils (0.24-1ubuntu1) ... (base) keddad@keddad:~$   But I didn't ask it to get me chromium via snap, I wanted to get a normal .deb package. It works, after all, but it just feels wrong. If I want to get a snap, I use snap, not apt. Why such behavior is considered normal?


Prove $\lim \limits_{n \to \infty}\frac{n!}{n^n}=0$.  I have tried this several ways.  I tried using the ratio test, I tried to expand it... I'm not really sure where to go.  When I expand, I get $$\frac{n(n-1)(n-2)(n-3).....}{nnnnnn......}$$ I don't know if trying to expand this is helpful, but I'm just not sure where to go with this problem... Any help would be appreciated.

I am trying to calculate the following limit without Stirling's relation.  \begin{equation} \lim_{n \to \infty} \dfrac{n!}{n^n} \end{equation} I tried every trick I know but nothing works. Thank you very much.


Solve this:     $$\int\sin(\cos x)dx$$   I checked on Maxima, mathematica but both cannot find its integral though numerical approximation is available in later. Has someone faced similar problem? Also, I saw that such problems are not stated in books also, no function can be expected to be invalid to integrate !!

I've been wondering, what is the general form for the integral of $\sin(\cos x)$? I tried integrating it myself and couldn't, tried with Wolfram Alpha and it couldn't either. If you think about it conceptually, it should have a general form as it's graph if just like sin and cos, which both have general forms. If it doesn't have a general form, I'd like to know why. Thanks!


I was having problems on my Macbook, getting my VPN service to start properly, and was they suggested that I create new Keychain and import settings into new Keychain. I did that, and now I am getting this constant pop-up message, saying autosd needs me to input my Keychain password.   Any ideas what is happening, how to fix this issue and stop the messages?

Ever since I changed my user account password, every time I log in to my machine I have to enter multiple passwords. First, I enter the new account password to actually log in. Once I'm at my desktop I get prompted to enter a few other passwords too. Namely the following:      My old password is required to successfully dismiss all of the above pop-ups. Is there some way of updating anything in my keychain that still uses the old password, to use the new password?  Any ideas what could have caused this? I can only imagine that the intended behaviour is for this update to happen automatically.


I am having dozens of MSSQL Servers 2012 R2 on Windows Server 2008 R2 with similar setup, configuration (in virtual machines) in production.  Neither has SSIS installed.   I have to similarly maintain (migrate, restore) the same maintenance plans on all of dozens servers    Any way to import-export-migrate-save-restore maintenance plans without having SQL Server Integration Service (SSIS) and Data Tools (BIDS) installed (and running)? Though I can stage a separate server machine for them    Saw  but still uncertain

I'm trying to export a simple maintenance plan from an SQL Server instance.  I want to check the export into source control, and apply the exported maintenance plan to functionally identical instances.   and  recommend using Integration Services to export the maintenance plan.  When I try to connect to Integration Services on the Export target, I receive the following error:     Connecting to the Integration Services service on the computer   "WEBSERVER" failed with the following error: The specified service   does not exist as an installed service.   We chose to disable Integration Services on WEBSERVER because we use this box only for serving data to consumer applications. All data on WEBSERVER is replicated from a backend instance. Integration Services is used heavily for processing data on the backend instance.  Is there a documented way to export a maintenance plan without using Integration Services? Does Microsoft support it?


I have a problem with this error message:  "Package minted Error: You must have `pygmentize' installed to use this package."  I read  but I don't overcome problem.  I installed Python 3.6 (32-bit). Can anybody help me? (I am dummy)

When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file


I have to compute the remainder of $15^{2098}$ divided by $14$, I know that the answer will be $1$ because $15$ is $14+1$ and the remainder of every $15$'s power will be $1$ when divided by $14$, the problem is that I can't write that as answer because it is not too mathematical, so I want know how can I prove this without having to do all the long computation.

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


I am trying to create a cartoon character with a simple mouth, but there are no tutorials that answer my question. Can I use a curve to animate a mouth? And if so, how can I?

Setting a fill and border is pretty easy in apps like Illustrator and Gravit Designer but in Blender. I've found it to be more tedious as I can't find anything online to solve this problem.  The picture above is a simple 2d mouth with lips. I would like to be able to move the lips and still have a fill but in Blender I needed to add another path for the mouth. Is there anyway I can move my lips path while having it also take the exact same shape (but not material) as my mouth's path?    (454.2 KB)  I work in Blender 2.79 cause 2.8 doesn’t run well on my laptop at all.


I have to generate a xml file dynamically at runtime. Please help me in generating the below XML file dynamically using PHP.  <?xml version="1.0" encoding="UTF-8"?> <xml>  <track>      <path>song1.mp3</path>      <title>Track 1 - Track Title</title>  </track>  <track>      <path>song2.mp3</path>      <title>Track 2 - Track Title</title>  </track>  <track>      <path>song3.mp3</path>      <title>Track 3 - Track Title</title>  </track>  <track>      <path>song4.mp3</path>      <title>Track 4 - Track Title</title>  </track>  <track>      <path>song5.mp3</path>      <title>Track 5 - Track Title</title>  </track>  <track>      <path>song6.mp3</path>      <title>Track 6 - Track Title</title>  </track>  <track>      <path>song7.mp3</path>      <title>Track 7 - Track Title</title>  </track>  <track>      <path>song8.mp3</path>      <title>Track 8 - Track Title</title>  </track>


This morning I've asked a question (on Academia) without registering. I've received an email with a link to set up an account and I've followed it. However it seems this new account is in no way connected with the question I've asked, so I can't comment/upvote/mark as accepted. Have I done anything wrong, or is it supposed to work that way? Is there any way to "merge" the accounts?

I accidentally posted a question without being logged in. Is there a way to associate that question with my account?   For more information, visit "" in the .   a.k.a. How can you link a registered account to a cookie-based account? a.k.a. How do I merge an unregistered account with a registered account a.k.a. Merging users a.k.a. How do I associate anonymous questions I’ve asked with my registered account? a.k.a. Is there a way to claim an unregistered user? (in case anyone searches with those terms)


I am new to C# and I want somthing that works like this in C++  #define PointCloud List<PointData>   wherer PointData is a small class which contains some data about a point and List is the generic List.  Greetings  //edit: PS: Is there a name for the thing I am searching? If there is one, please tell me.

I want to create an alias for a class name. The following syntax would be perfect: public class LongClassNameOrOneThatContainsVersionsOrDomainSpecificName {    ... }  public class MyName = LongClassNameOrOneThatContainsVersionOrDomainSpecificName;  but it won't compile.  Example Note This example is provided for convenience only. Don't try to solve this particular problem by suggesting changing the design of the entire system. The presence, or lack, of this example doesn't change the original question. Some existing code depends on the presence of a static class: public static class ColorScheme {    ... }  This color scheme is the Outlook 2003 color scheme. i want to introduce an Outlook 2007 color scheme, while retaining the Outlook 2003 color scheme: public static class Outlook2003ColorScheme {    ... }  public static class Outlook2007ColorScheme {    ... }  But i'm still faced with the fact that the code depends on the presence of a static class called ColorScheme. My first thought was to create a ColorScheme class that I will inherit from either Outlook2003 or Outlook2007: public static class ColorScheme : Outlook2007ColorScheme { }  but you cannot inherit from a static class. My next thought was to create the static ColorScheme class, but make Outlook2003ColorScheme and Outlook2007ColorScheme classes non-static. Then a static variable in the static ColorScheme class can point to either "true" color scheme: public static class ColorScheme {     private static CustomColorScheme = new Outlook2007ColorScheme();     ... }  private class CustomColorScheme  {     ... }  private class Outlook2008ColorScheme : CustomColorScheme  {     ... }  private class Outlook2003ColorScheme : CustomColorScheme  {    ... }  but that would require me to convert a class composed entirly of readonly static Colors into overridable properties, and then my ColorScheme class would need to have the 30 different property getters thunk down into the contained object. That's just too much typing. So my next thought was to alias the class: public static ColorScheme = Outlook2007ColorScheme;  But that doesn't compile. How can I alias a static class into another name?  Update: Can someone please add the answer "You cannot do this in C#", so I can mark that as the accepted answer. Anyone else wanting the answer to the same question will find this question, the accepted answer, and a number of workarounds that might, or might not, be useful. I just want to close this question out.


How can I check if two lines (created with function love.graphics.line) are crossing themselves? I may use this ability to create procedural maps via graphs.

I have two lines say P1( 0, -1, 0, -1 ) and P2( -1, 0, 0, -1 ). Since I'm working in 2D, there is no Z component. The x,y,z components are normals and the w component is the distance from origin. I am not given the origin or any points on the line.  What method should I use to programmatically determine the point of intersection for these two lines?


← Vote up if you think this post is helpful.   That's an example. I often see such requests in comments, but not sure if it's suitable in post body.

I searched duplicates, and my impression was that requests may be acceptable, or at least tolerated, after questioner has indicated the answer solved his problem, and with the request for points via a comment.  For example, this discussion:   However, my question is slightly different.  Is it OK to include the request for points within the initial answer?  "Don't forget to tip your waiter by clicking on the checkmark next to my answer if this is useful. :o)"    In that example, the request wasn't demanding.  It was humorous.  Does that make a difference?  But since the request doesn't contribute to the usefulness of the answer, does it belong in the answer at all?  If it's not acceptable as part of the answer, would it be OK as a comment instead, and when submitted immediately after the answer?


Why do galaxies over time become more refined, ordered and defined instead of more random and disordered?

I've heard most of galaxies are spiral or ellipsoid shaped. Is it true?  If true, then why they form in such shapes?  How did arms of the spiral galaxies form?


I just arrived in Germany for the 4th time. I made tea in break of the work meeting, and at the very end of it, I found small solid pieces... I thought that the cup was too old and maybe was starting to lose its "material". A guy told me that this because of the water being "too heavy" here in Germany, and he doesn't drink it, but filters the water through a machine, and then drinks it.  During my first trip, I asked if it is OK to drink tap water in my hotel, and they said yes, but we don't drink it, we buy mineral water from the market. And from all the people I have asked here, this is what I get as an answer, more or less.  My mother told me that the water in Germany is not drinkable, because it has too much iron. I think here they call it kalk, which seems to be some metal in any case.  The knowledge of my mother is likely to be outdated, and while searching the Internet, I see that the situation has changed across the years, and that now it's safe to drink tap water, which contradicts what people say in real life. I am very confused.  So, is it safe to drink tap water in Germany? Nobody gives a boolean answer which makes me worry! If area matters, we travel in Munich and nearby towns, all parts of Bavaria.

Before moving to Munich I did some research about the water. According to different sources, the water quality in Munich is very good and there is no problem drinking it.  But every time I'm in a store I see locals buying large amounts of bottled water. Is there a reason for that?


Prove that $f = a_nx^n + \cdots + a_1x+a_0$ is a unit in $R[x]$ if and only if $a_0$ is a unit in $R$ and $a_1, ..., a_n$ are nilpotent.   My argument is as follows.   Suppose that $f$ is a unit in $R[x]$ and consider the evaluation map $\varphi : R[x] \to R$ defined by $x \mapsto 1$. We therefore have that $\varphi(f) = (a_n + \cdots + a_1) + a_0$. We note that Question 1 gives us that the sum of a nilpotent element and a unit is a unit. We therefore conclude that since $\varphi$ must map a unit in $R[x]$ to a unit in $R$, $(a_n + \cdots + a_1) + a_0$ is a unit in $R$. Furthermore, with the some of nilpotent elements being nilpotent, this yields that $a_1, ..., a_n$ are nilpotent and $a_0$ is a unit in $R$.   My argument lacks rigour in showing that $(a_n + \cdots a_1)$ must be nilpotent and $a_0$ must be the unit. I simply state this, which I'm not satisfied with. Could I take another evaluation map, this time evaluating at $x=0$?  Furthermore, the other direction seems unclear given that I cannot consider something as simple as an evaluation map.   Also note that this question is not a duplicate. The induction argument that is used almost ubiquitously as a solution is not intuitive and therefore I want to prove it through this approach of evaluation maps.

Let $R$ be a commutative ring. Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent if and only if $a_0,a_1,a_2,\ldots,a_n$ are nilpotent.   Now since $f(x)$ is nilpotent then $f^n=0$ for some $n$. Now $f^2=c_0+c_1 x+\cdots+c_n x^n$ where $c_i=\sum _{k=0}^i  a_k a_{i-k}$.  But how to write it for $f^n$? How to take it from here?  If $n_i$ be the least positive integer such that $a_i^{n_i}=0$ then  what will the positive integer such that $a_i^n=0$ for all $i$??


I would like to find out if there is any way of making code to create and open folders in python, I've looked around the web but I can't seem to find anything that's simple and can be implemented into current code. Is there  a way of doing it like making a text file or a different way? If there is, let me know. Thanks!

What is the most elegant way to check if the directory a file is going to be written to exists, and if not, create the directory using Python? Here is what I tried:  import os  file_path = "/my/directory/filename.txt" directory = os.path.dirname(file_path)  try:     os.stat(directory) except:     os.mkdir(directory)         f = file(filename)   Somehow, I missed os.path.exists (thanks kanja, Blair, and Douglas). This is what I have now:  def ensure_dir(file_path):     directory = os.path.dirname(file_path)     if not os.path.exists(directory):         os.makedirs(directory)   Is there a flag for "open", that makes this happen automatically?


It's a nice habit to return *this from a class' methods, so that method calls can be chained. Consider this example:  template <typename T> class container  { public:   container& append(const T& x) {      ...     return *this;    } };  container<int> a; a.append(1).append(2).append(5);   However, when a new class is derived from this, it breaks the chain:  class int_container : public container<int>  { public:   int_container& sort_ascending()  {     ...     return *this;   } };  int_container b; b.append(10).sort_ascending();   // error: container::sort_ascending() does not exist   This can be solved by replicating the base class' methods and updating the return type ...  class int_container : public container<int>  {   int_container& append(int i)  { container<int>::append(i); return *this; }   ... };   ... but well, my base class has 60 of such methods and I need several derived classes. So, is there any way to update the return type of those methods in derived classes, without having to override each single method in each derived class? And without using preprocessor macros?

Consider:  // member data omitted for brevity  // assume that "setAngle" needs to be implemented separately // in Label and Image, and that Button does need to inherit // Label, rather than, say, contain one (etc)  struct Widget {     Widget& move(Point newPos) { pos = newPos; return *this; } };  struct Label : Widget {     Label& setText(string const& newText) { text = newText; return *this; }     Label& setAngle(double newAngle) { angle = newAngle; return *this; } };  struct Button : Label {     Button& setAngle(double newAngle) {         backgroundImage.setAngle(newAngle);         Label::setAngle(newAngle);         return *this;     } };  int main() {     Button btn;      // oops: Widget::setText doesn't exist     btn.move(Point(0,0)).setText("Hey");      // oops: calling Label::setAngle rather than Button::setAngle     btn.setText("Boo").setAngle(.5);  }   Any techniques to get around these problems?  Example: using template magic to make Button::move return Button& or something.  edit It has become clear that the second problem is solved by making setAngle virtual.  But the first problem remains unsolved in a reasonable fashion!  edit: Well, I guess it's impossible to do properly in C++. Thanks for the efforts anyhow.


I recently went searching to see if there was a Stack Exchange site about relationships and found . Unfortunately, I have no way of pledging my support, as it was closed three years ago.  Is there a way to vote for a site to be reopened? I'd love to pledge my support and help give good site ideas a second chance.

We in the Selenium community were  at Area 51.  Of late there was discussion about .  There was great opposition from the Selenium community to merging with the more general software testing proposal.  We got notified today that the Selenium proposal has already been merged with the software testing one.  Also that the Selenium proposal has been closed, which is very very sad.  We want to know -   When there was great discontent about the merge, why did the merge still happen? How could we reopen the Selenium proposal? If SE sites are all about openness then why was such an autocratic decision made?   Remember we already have Google-Groups for Selenium users which receives the highest amount of traffic for Selenium qs.  The idea was to close Google-Groups once we had a dedicated Selenium area51 site.  When we don’t have a dedicated Selenium site, Google-Groups would also continue and there would be fewer questions on Selenium asked on the new merged site, or on any other site for that matter.  Refer  which shows how helpless we feel.


The image shown below is the output for plot(lm.fit) on the Boston dataset, where lm.fit=lm(medv~lstat) . Why are some of the points labelled in the plot ?

I had a question about interpreting the graphs generated by plot(lm) in R.  I was wondering if you guys could tell me how to interpret the scale-location and leverage-residual plots?  Any comments would be appreciated.  Assume basic knowledge of statistics, regression and econometrics.


Please tell me the various resolution in different sizes.

For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print?


Do features that allow you to add twice your proficiency bonus, under some other name, stack with Expertise?  For instance, , with  as applied to History checks, to identify the origin of stonework.  The text of Stonecunning is reproduced below:     Whenever you make an Intelligence (History) check related to the origin of stonework, you are considered proficient in the History skill and add double your proficiency bonus to the check, instead of your normal proficiency bonus.   And, for good measure, the relevant portion of Expertise:     Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.

Let's say I'm a multiclass rogue/ranger and I have taken Expertise in survival checks. Now, if a ranger is in their favored terrain it says they double their proficiency bonus in intelligence and wisdom checks relating to you environment. If I am in my favored terrain and use my already doubled survival check, will it double again?


Is it still safe to eat? It was cooked the other day, reheated last night, and left in the oven until 4:30, turned off of course.

If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?


I have an idea for working with geospatial rasters to predict housing prices.  I have done this before using mulitivariate linear regression.  I would like to try using a convolutional neural network.  I have a series of rasters that represent a surface of interpolated housing prices over time.  The convolutional neural network will learn from the price rasters, but I need to add in other explanatory variables. The most important is time.  I might add additional scalar values such as interest rate or stock market.  I might also want to add additional rasters as regressors, such as crime maps, or distance to transit.  I know that in a typical neural network regression there is one neuron per explanatory variable, and in a typical CNN there is a neuron per pixel on the input layer.  So I would like some regressors to be rasters, and some to be scalers.  My question is how do I add additional explanatory variables, both rasters and scalars, to a convolutional neural network?  I am using Keras and TensorFlow.


I am learning C++ and I want to know what is more efficient for debugging;  Is std::cout << "Test\n"; more efficient than std::cout << "Test" << std::endl?  What I am trying to say here is, is "<string>\n" more efficent then <string> << std::end;?

Many C++ books contain example code like this...  std::cout << "Test line" << std::endl;   ...so I've always done that too. But I've seen a lot of code from working developers like this instead:  std::cout << "Test line\n";   Is there a technical reason to prefer one over the other, or is it just a matter of coding style?


I am a US citizen and want to travel across Europe by myself after graduation, but I wont be 18 yet. Would I have a problem traveling through countries? Is there anything specific I would need from my parents, like a note? Are there places I can stay that I can book by myself, like youth hostels? I want to take the eurorail the whole way, would traveling by myself be a problem?

So I'm a 15 year old teenager who moved to Germany like 6 months ago (with my family of course) and I was wondering if I could travel alone back to my hometown in Croatia for a few days with a bus during my upcoming school holidays. Of course I have my grandmother to take care of me there. (The trip would be long around 20 hours so from Freiburg to Vukovar)


Find $$\lim_{x\to \infty}\left({x \over x^2+1}+{x  \over x^2+2}+\cdots +{x\over x^2+x}\right)$$ , without using squeeze theorem. I have done the solution as below using squeeze theorem ... $$Let \left[\left({x \over x^2+1}+{x  \over x^2+2}+\cdots +{x\over x^2+x}\right)\right]=f(x)\implies \\  \left({x \over x^2+x}+{x  \over x^2+x}+\cdots +{x\over x^2+x}\right)\lt f(x)\lt \left({x \over x^2+1}+{x  \over x^2+1}+\cdots +{x\over x^2+1}\right) \\ {x^2 \over x+x^2}\lt f(x) \lt {x^2\over 1+x^2}\\ \text{applying limit on both sides }\\ \implies\lim_{x\to \infty}{x^2 \over x+x^2}= \lim_{x\to \infty}{x^2\over 1+x^2}=1\\ \implies \lim_{x\to \infty}f(x)=1$$  Can we do this without squeeze theorem?

Sum of $$\lim_{n\rightarrow \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+2}+\cdots \cdots \cdots +\frac{n}{n^2+n}\right)$$  $\bf{My\; Try::}$ I have solved it  using Squeeze theorem  $$\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{n}{n^2+n}\leq \lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{n}{n^2+r}\leq \lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{n}{n^2+1}$$  So we get $$\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{n}{n^2+r} = 1$$  My question is can we solve above limit without using Squeeze Theorem,   If yes then plz explian me, Thanks


I am not that punctuation-savy, so I have one question for my research title.  Currently it is      Social crowdfunding:  individual- and project-related determinants of success.    Empirical investigation on Kickstarter   Here I have two questions.   Is it right to say individual- or just individual?  Should there be a period after "Empirical investigation on Kickstarter"?

If multiple hyphenated terms share the same latter half, and I wish to list them without repeating that latter half, how should the hyphens be placed?  For example:     I will be investigating control issues in ground-based, water-based, and air-based robots.   If I do not want to repeat based, could I write:     I will be investigating control issues in ground-, water-, and air-based robots.   Is it correct to just leave a hyphen dangling after ground and water?  If not, how should it be written? I know the original sentence doesn't sound too bad, but I really just want to know the punctuation rule (or the convention in American English if there is no rule).


Test code:  @RunWith(RobolectricTestRunner.class) @Config(constants = BuildConfig.class) public class MainActivityTest { private MainActivity mainActivity;  @Test public void testMainActivity() {     MainActivity mainActivity = Robolectric.setupActivity(MainActivity.class);     mainActivity.findViewById(R.id.visual_button).performClick();     Intent expectedIntent = new Intent(mainActivity, VisualActivity.class);     ShadowActivity shadowActivity = Shadows.shadowOf(mainActivity);     Intent actualIntent = shadowActivity.getNextStartedActivity();     Assert.assertEquals(expectedIntent, actualIntent); } }   error reports:  java.lang.NullPointerException   my Robolectric version is 3.1.4... l have tried to find some solutions but failed. l'm sure that my test code are under src/test, not src/androidTest, can anybody help me ? Thanks in advance!

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I cannot ensure whether column space of $A^TA$ is the same as $A^T$, if it is, how to prove?

Suppose we have a $n \times m$ rectangular matrix $A$ with row space $\text{row}(A)$ and column space $\text{col}(A)$.   What are the row spaces and the column spaces of $A^T A$ and $A A^T$?


I'm about to put my house on the market, and I'd like to hear some tips for making the best possible photographs, specifically for this purpose.  Among things I should like to hear comments about are these:   Use a fairly wide-angle lens Use low ISO and small aperture for sharpness and low noise (of course, this implies a tripod and long exposures)   Tweak the colour temperature to make the interiors "glow"? Plus, of course, any other suggestions   FWIW, I'm using an EOS-M, probably with the 11-22mm lens (though I could also use one of the other two EF-M lenses), with DXO Optics Pro for post-processing.  I appreciate there isn't one single 'right' answer to this, but I couldn't find a button to turn it into a community wiki question. Anyone with the right combination of authority and opinion, please feel free to do so.

Specifically, I might be taking pictures inside of a house that's for sale. I want to make them look as best as possible.  While I think it'd be nice to have general answers, let me just give you some of my gear, that I think would be the best I have towards photography.   Canon 20D 580 EX II Flash 28-135mm lens   I'm interested in both gear and in general advice.


I am kind of new to programming and unsure what I have done wrong with my code. The error is logcat is as follows      Caused by: java.lang.NullPointerException: Attempt to invoke virtual method 'void com.google.android.material.bottomnavigation.BottomNavigationView.setOnNavigationItemSelectedListener(com.google.android.material.bottomnavigation.BottomNavigationView$OnNavigationItemSelectedListener)' on a null object reference         at com.example.cleverreality.MainActivity.onCreate(MainActivity.java:42)  And this is the code for fragments I have been working on with the error on the 2nd line.         BottomNavigationView bottomNav = findViewById(R.id.bottom_navigation);         bottomNav.setOnNavigationItemSelectedListener(navListener);     }     private BottomNavigationView.OnNavigationItemSelectedListener navListener =             new BottomNavigationView.OnNavigationItemSelectedListener() {                 @Override                 public boolean onNavigationItemSelected(@NonNull MenuItem item) {                     Fragment selectedFragment = null;                      switch (item.getItemId()) {                         case R.id.home:                             selectedFragment = new HomeFragment();                             break;                         case R.id.settings:                             selectedFragment = new SettingsFragment();                             break;                         case R.id.devices:                             selectedFragment = new DevicesFragment();                             break;                     }                 getSupportFragmentManager().beginTransaction().replace(R.id.fragment_container,                         selectedFragment).commit();                      return true;                 }             };  Any help would be greatly appreciated.


If I have a rod,made of some metal,what experiment should I perform to check whether or not the mass is evenly distributed in the rod i.e how to check whether it has the same density all over?

How can I determine whether the mass of an object is evenly distributed without doing any permanent damage? Suppose I got all the typical lab equipment. I guess I can calculate its center of mass and compare with experiment result or measure its moment of inertia among other things, but is there a way to be 99.9% sure?


I'm a learner and creating my first website. after adding a login and add new user forms to my website, i came to know that I must not save my passwords in DB as plaintext. I did some search and find out about md5(), salt, encryption etc etc. Most of my finding were from this same site but there were more long long codes, which I couldn't understand clearly. In short I want to know what modifications i must do to my code (given below)?  Adding new user/Admin form:  <form action="add_user.php" method="post"> New User Name : <input type="text" name="username" placeholder = "New User Name">
 New Password :<input type="password" name="password" placeholder = "New Password">
  Confirm Password :<input type="password" name="againpassword" placeholder = "Enter Password Again">

 <input type="submit" value="Save" name="Submit-Event" style="font-size:16px"><input type="reset" value="Reset" style="font-size:16px">
 </form>   php file: add_user.php  <?php $server="localhost"; $user="root"; $password=""; $database="camouflage_studio";  $con = mysqli_connect($server,$user,$password,$database); if (mysqli_connect_errno())   {   echo "Connection Error: " . mysqli_connect_error();   }  //check if password matches $firstpassword = $_POST['password']; $secondpassword = $_POST['againpassword']; $username = $_POST['username'];  if(($firstpassword == $secondpassword) and $firstpassword !== '' and $username !== '') {     // prepare and bind     $stmt = $con->prepare("insert into users (username, password) VALUES (?, ?)");     $stmt->bind_param("ss", $_POST['username'], $_POST['password']);     if(mysqli_stmt_execute($stmt))     {     echo '';     }     else     echo "Prepare Error: ",$con->error;     //remove $con->error before making ONLINE THE CODE. }  else     {       echo '';      } $stmt->close(); $con->close();  ?>

It is currently said that MD5 is partially unsafe. Taking this into consideration, I'd like to know which mechanism to use for password protection.  This question,   suggests that hashing multiple times may be a good idea, whereas  suggests using salt.  I'm using PHP. I want a safe and fast password encryption system. Hashing a password a million times may be safer, but also slower. How to achieve a good balance between speed and safety? Also, I'd prefer the result to have a constant number of characters.   The hashing mechanism must be available in PHP It must be safe It can use salt (in this case, are all salts equally good? Is there any way to generate good salts?)   Also, should I store two fields in the database (one using MD5 and another one using SHA, for example)? Would it make it safer or unsafer?  In case I wasn't clear enough, I want to know which hashing function(s) to use and how to pick a good salt in order to have a safe and fast password protection mechanism.  Related questions that don't quite cover my question:


Let $X_{1},X_{2},X_{3}....X_{n}$ be independent and identically distributed random variables with continuous density symmetric around 0. Also suppose $\mathbb{E}(|X_{1}|)$=2. Define two variables Y and Z as $Y=\sum_{i=1}^{n}X_{i}$ and $Z=\sum_{i=1}^{n}$1$_{X_{i}>0}$ We are asked to find the covariance between Y and Z. My approach: As $X_{i} $ has symmetric density around 0, $\mathbb{P}(X_{i}>0)=\frac{1}{2}$ and because Z is an indicator function for each $X_{i}$ being greater than 0, Z $\sim$ Bin(n,$\frac{1}{2}$). Because $\mathbb{E}(|X_{i}|)$=2, $\int_{0}^{\infty}xf_{x}(x) dx=1$ and $\int_{-\infty}^{0}xf_{x}(x) dx=-1$ Which means that expectations of $x$ given $x$ is positive or negative are 1 and -1 respectively. Now $\mathrm{Cov}(Y,Z)=\mathbb{E}(YZ) - \mathbb{E}(Y)\mathbb{E}(Z)$, let’s call $W=f(Y,Z)=YZ$, using law of iterated expectations with a slight abuse of notation $\mathbb{E}(W)=\mathbb{E}(\mathbb{E}(W|Z=r)$, where the first expectation on right is with respect to the marginal of Z and inner expectation is with respect to conditional distribution of W with for a given Z=r. For the inner expectation, given a value of Z=r, the term in Z would have exactly $r$ $1$’s and $n-r$ $0$’s which would be multiplied with each $X_{i}$ term in Y so $W|(Z=r)=r(\sum_{i=1}^{n}X_{i})$ so that the inner expectation becomes $\mathbb{E}(W|Z=r)=r\mathbb{E}(\sum_{i=1}^{N}X_{i})$. The expectation on right has exactly $r$ times $1$’s and $n-r$ times $-1$’s corresponding to $X_{i}$ being positive $r$ times with expectation of $1$ and negative $n-r$ times with expectation of $-1$. So $\mathbb{E}(W|Z=r)=r(2r-n)=2r^{2}-rn$ Since Z$\sim$ Bin(n,$\frac{1}{2}$), $\mathbb{E}(Z)=\frac{n}{2}$, $\mathrm{Var}(Z)=\frac{n}{4}$ so $\mathbb{E}(Z^{2})=\frac{n}{4}+\frac{n^{2}}{4}=\frac{n(n+1)}{4}$ Hence the final expression becomes $\mathbb{E}(W)=2\mathbb{E}(r^{2})-n\mathbb{E}(r)=\frac{n^{2}+n}{2}-\frac{n^{2}}{2}=\frac{n}{2}$ And since $\mathbb{E}(Y)=0$ due to symmetric density around 0, $\mathrm{Cov}(Y,Z)=\mathbb{E}(W)-\mathbb{E}(Y)\mathbb{E}(Z)=\frac{n}{2}$ Is the above approach correct for finding the covariance between Y and Z? Any suggestions/corrections will helpful

The question is-     Let $X_1,X_2,..,X_n$ be iid random variables from a continuous distribution whose density is symmetric about $0$. Suppose $\mathbb{E}(|X_1|)=2$ and define $Y=\sum_{i=1}^{n}X_i$ and $Z=\sum_{i=1}^{n}I(X_i>0)$. Then calculate covariance between $Y$ and $Z$.   My attempt:  $E(X_i)=0$ for all $i=1(1)n$ because $X$ is symmetric about $0$ and $E(|X|) $ exists.   Now,  $Cov (Y,Z)=E(YZ)-E(Y)E(Z)$ $=E(YZ)-0$ $=E[(\sum_{i=1}^{n}X_i)(\sum_{i=1}^{n}I(X_i>0)]$  $=(\sum_{i=1}^{n}E[(X_i.I(X_i>0))]$ $+\sum\sum_{i \neq j}E(X_i)E(I(X_j>0)$ as $X_i,X_j$ are independent.   $=\sum_{i=1}^{n}E[(X_i.I(X_i>0)] +0 $ as $E(X_i)=0$  $ =\sum_{i=1}^{n}\{E[X_i.I(X_i>0)|I(X_i>0)=1]×1/2] + E[X_i.I(X_i>0)|I(X_i>0)=0]×1/2]\}$  $=\sum_{i=1}^{n}E[X_i.I(X_i>0)|I(X_i>0)=1]×1/2] +0$  $=\sum_{i=1}^{n}E[X_i|X_i>0]×1/2]$  $=2n×(1/2)$ $=n$  Is my reasoning correct ? Thanks in advance!


Let $A$ be $2 \times 2$ matrix with trace 2 and determinant -3. Let $T:M_2(\mathbb{R})\to M_2(\mathbb{R})$ defined by$T(B)=AB$. Then How to show that $T$ is diagnalizable? Could you please give me some hints?

$A$ be a $2\times 2$ real matrix  with trace $2$ and determinant $-3$, consider the linear map $T:M_2(\mathbb{R})\to M_2(\mathbb{R}):=B\to AB$ Then which of the following are true?   $T$ is diagonalizable $T$ is invertible $2$ is an eigen value of $T$ $T(B)=B$ for some $0\ne B\in M_2(\mathbb{R})$    if $ A=\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}$ Then I have calculated that matrix of $T$ will be \begin{pmatrix}a_{11}&a_{12}&0&0\\a_{21}&a_{22}&0&0\\0&0&a_{11}&a_{12}\\0&0&a_{21}&a_{22}\end{pmatrix} so $T$ is invertible I can say as $\det T=(\det A)^2=9$, could any one help to find out others as true/false?


I have a website which is actually a search engine to search through our data. Each item has its own detailpage, and a search returns a list of matching data, with links to the detailpages. There are about 10 million items in our database, however, every day several hundreds are removed, and new ones are added. The new ones are no problem, but how should I treat the removed ones? Currently, I'm giving them a status 404, but Google is constantly complaining about this in the webmaster tools. I was thinking about two options: a 410 (REALLY gone), or make it a redirect (301) to the homepage?

Before asking my question, I'll use an example to clarify the idea.  Say that a company used to sell horses and then they turn into a sheeps business. While some of the old pages can be mapped to the new pages using a 301 redirect, because they're really related in the content and the company don't want to lose users and link juice, there are a lot of pages strictly related to horses that they want to shutdown.  What's the best practice? Is there a way to say to users and Search Engines the content you were looking for won't be available any more?  Basically a 301 redirect of the closed pages to new ones seems not so good, because you'll show a content totally unrelated to the searched one.  P.S: I'm aware that probably the best fallback is to simply map those pages to the homepage but I hope in a smarter solution.


Conceptually, aren't the eigenvalues of a correlation matrix and the singular values of the associated scaled data matrix supposed to be the same? The below illustration is saying that it isn't so. Please point out what I am missing.  > M      [,1] [,2] [,3] [1,]    1    6   11 [2,]    2    7   12 [3,]    3    8   21 [4,]    4    9   14 [5,]    5   10   34 > M.scale = scale(M) > M.cor.eigen = eigen(cor(M)) > M.prcomp = prcomp(M.scale) > M.svd = svd(M.scale) > M.cor.eigen$values     [1] 2.729542e+00 2.704577e-01 1.198779e-16     > M.prcomp$sdev ^ 2 [1] 2.729542e+00 2.704577e-01 5.960165e-34 > M.svd$d [1] 3.304265e+00 1.040111e+00 1.953076e-16

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SVD and PCA?  Or in other words, how to use SVD of the data matrix to perform dimensionality reduction?


I've used HDDScan and I found a LOT of bad sectors, but only on a specific portion of my disk. Probably the problem is isolated, I hope.  I'd like to 'move' data from this sectors, because I know that a bad sector can be read, but not written. Is there a software that automatically, when found bad sectors will move, preserving, the data in these sectors to a more safest place?  Data preservation is fundamental for me.

If I know that a hard disk has bad sectors, how can I "mark" them so that Windows 7 doesn't write to them when I copy files and stuff?


I'm trying to run   $ sudo apt-get upgrade   and here is the output  $ Reading package lists... Done Building dependency tree        Reading state information... Done Calculating upgrade... Done The following packages have been kept back:   linux-generic-lts-utopic linux-headers-generic-lts-utopic   linux-image-generic-lts-utopic linux-tools-virtual-lts-vivid The following packages will be upgraded:   apparmor apport apport-gtk bash-completion bind9-host   chromium-codecs-ffmpeg-extra dnsutils firefox firefox-locale-en   flashplugin-installer gir1.2-gdkpixbuf-2.0 gir1.2-gtk-3.0 libapparmor-perl   libapparmor1 libbind9-90 libdns100 libexpat1 libexpat1:i386 libgail-3-0   libgdk-pixbuf2.0-0 libgdk-pixbuf2.0-common libgtk-3-0 libgtk-3-bin   libgtk-3-common libisc95 libisccc90 libisccfg90 liblwres90   libnautilus-extension1a libnss-winbind libpam-winbind libsmbclient   libsnmp-base libsnmp30 libvdpau1 libwbclient0 linux-firmware linux-libc-dev   linux-tools-common nautilus-data oneconf oneconf-common openssh-client   oracle-java8-installer python-oneconf python-samba python3-apport   python3-oneconf python3-problem-report samba samba-common samba-common-bin   samba-dsdb-modules samba-libs samba-vfs-modules smbclient ssh-askpass-gnome   tlp tlp-rdw tzdata winbind xul-ext-ubufox 62 upgraded, 0 newly installed, 0 to remove and 4 not upgraded. Need to get 0 B/81.5 MB of archives. After this operation, 6,653 kB of additional disk space will be used. Do you want to continue? [Y/n] y Extracting templates from packages: 100% Preconfiguring packages ... dpkg: warning: files list file for package 'liba52-0.7.4' missing; assuming package has no files currently installed E: Sub-process /usr/bin/dpkg returned an error code (2)

I want to install Open JDK or Oracle JDK to my machine but I got an error during installation. The error is:  Selecting previously unselected package oracle-java8-installer. dpkg: warning: files list file for package 'unity-scope-gourmet' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-guayadeque' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-gmusicbrowser' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-manpages' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-firefoxbookmarks' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-gdrive' missing; assuming package has no files currently installed dpkg: warning: files list file for package 'unity-scope-home' missing; assuming package has no files currently installed E: Sub-process /usr/bin/dpkg returned an error code (2)   I searched on Google and try to something for install/reinstall this packages. Finally i try to remove Unity. I faced this error for my every tries. I am using Xmonad. How can I fix this issue?


I have a laptop that when I have it on my desk, it's connected to a usb wifi adapter. However, whenever I bring it anywhere else I use the internal wifi card. But this means I have 2 interfaces, both enabled, and connected. So to make sure when I am using the correct one when I am at my desk, I go into the adapter settings and disable the internal wifi interface. I am looking to create something to speed up the process, as well as learn about command line scripting!  I am trying to create a batch file to do the following: Note: WiFi = USB adapter. Always use this if connected. Wi-Fi 2 = internal wifi interface. Only use if the other is disabled or not connected    1) Check to see which NIC adapter is enabled/connected.  netsh interface show interface 2) Create an IF statement -    - IF WiFi is enabled and connected - disable Wi-Fi 2    - ElseIf WiFi is not enabled - enable Wi-Fi 2    However, I am not sure how to do this in CMD. Any pointers? Is there something else I need?

Is there a way to enable/disable a wireless network interface via the command line (so I can put it in a bat file)?  When I'm in the office I use a wired connection, but Windows still occasionally bugs me about my wireless connection not being connected (even though I turned off the option for notifying me when there's no connectivity).  I'm guessing the only way to stop it from bugging me is to disable the interface, but I'd rather not have to go into the network settings every time I need to do so.  I'd like to set up a bat file or a shortcut that I can use to enable/disable the wireless (preferably a single one that toggles the current state), and then just set up a keyboard shortcut for that.  I just have no idea how to do so from the command line.


I've created that new macro:  \newcommand{\undbf}[1] {\textbf{\underline{\smash{#1}}}}   To get underline closer to letters but, for instance with this code:  \documentclass[8pt,a4paper,dvipsnames]{article} \usepackage[utf8]{inputenc}   \newcommand{\undbf}[1] {\textbf{\underline{\smash{#1}}}}  \begin{document} \undbf{StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange, StackExchange,} \end{document}   I've not got line-breaking automatically; I mean:    And I would like could underline text in that way but have got automatic new lines. Thank you so much :)

I am currently using \underline{...} to underline text.  However, I want the underline to be closer to the letters (as of now, there's too much whitespace between the letters and the line).  Is there a simple way to do this?


An answer to previous  on link rots indicated that they are best fixed by user edits. Such edits are limited to a minimum of 6 characters, which is sometimes not the case with link rots. So how should they be fixed?

At present a low rep user (under 2k) can only make an edit suggestion of more than 6 chars, however when someone has taken the time to find to correct link it is a real shame the correction can help other users!  So I think link fixing should be special cased somehow.  (Also the checkering of a changed link need to be better than other edits, so a page that showed what both the old a new links point to (in frames) could help with the approving processes.)


I was curious whether The Borg had ever encountered Odo's species, and would be possible to assimilate them?

Are there any works, canon or otherwise, that deal with the concept of the Founders, or other shapeshifters, being assimilated or otherwise encountering the Borg?  The idea of an assimilated Founder just came to me, and the difficulty of inserting nanoprobes into a non-solid mass interests me. I suspect the answer to this question is negative, but am curious.


"When I was a child, I must eat everything on my plate or I wouldn’t get any dessert." Find a part of the sentence that contains a mistake.

I have seen uses of must that appear to be in the simple past tense. Sometimes these seem grammatical, but sometimes not. Examples that help illustrate my confusion:     He knew he must go to New York - sounds fine to me.      He went to New York because he must - sounds questionable.      Because he must go to New York, he bought plane tickets - sounds completely ungrammatical.      He must go to New York - grammatical, but with no other verbs to provide context, can't interpret this as being past-tense.   My question: is this past-tense use of must ever acceptable? Is it only acceptable in certain contexts - if so, what are those contexts and why?  (Note - I'm not looking for had to. Have is a different verb, so had to expresses the same meaning as the past tense of must, but it itself is not the past tense of must.)


From some months I have been solving a problem but I cannot finish. My question is, "How can I extract a road centreline from delaunay triangulation using open-source QGIS?" Actually, I am using Chugiak.

I was wondering if there is a way to create centre lines from polygons in QGIS? I have a polygon layer, but ideally need the centrelines as a separate file.


I am trying to get my footer stick to the bottom of the website, I haven't seen a good answer for making the footer stick to the bottom, when the page height is less than the viewport height and when the viewport height is less than the page height.

I have a simple 2-column layout with a footer that clears both the right and left div in my markup.  My problem is that I can't get the footer to stay at the bottom of the page in all browsers.  It works if the content pushes the footer down, but that's not always the case.


I'm new to programming. First, the following is my code:  x = 11  def f():     x = 22     print(x)     class C:         print(x)  f()   I got three printed results, "22 22", as output. When I changed my code like this:  x = 11  def f():     x = 22     print(x)     class C:         print(x)         x = 33         print(x)  f()   I got "22 11 33" instead of what I'm expecting: "22 22 33".  It seems like when I add a local x in the nested class, the order of variable searching is changed. I believe there's some tricks about scopes that I don't know yet. Can anyone explain this to me?

What exactly are the Python scoping rules?  If I have some code:  code1 class Foo:    code2    def spam.....       code3       for code4..:        code5        x()   Where is x found?  Some possible choices include the list below:   In the enclosing source file In the class namespace In the function definition In the for loop index variable Inside the for loop   Also there is the context during execution, when the function spam is passed somewhere else. And maybe  pass a bit differently?  There must be a simple reference or algorithm somewhere.  It's a confusing world for intermediate Python programmers.


I am trying to understand how to do proof by induction for inequalities. The step that I don't fully understand is making an assumption that n=k+1. For equations it is simple. For example:     Prove that 1+2+3+...+n = $ \frac {n(n+1)}{2} $ is valid for $ i \ge 1 $     1) Base case for n=1. (...)  2) Assume that equation is true for n=k. (...)  3) Proof for n=k+1. 1+2+3+...+k+(k+1) = $ \frac {(k+1)[(k+1)+1]}{2} $  So we add +1 to k on both sides.  For inequalities: Prove that $ 4n \lt 2^n $ is valid for $ n \ge 5 $  1) Base case. (...)  2) n=k assumption. (...)  3) n=k+1 proof.    How I would do this(add 1 to k on both sides): $ 4(k+1) < 2^{k+1} $  How it's done in tutorials: $ 4(k+1) < 2^k + 4 $ $ 4k+4 < 2^k + 4 $  Why they add extra 4 to RHS instead of increasing k by 1?

Apparently $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$.  How? What's the proof? Or maybe it is self apparent just looking at the above?   PS: This problem is known as "The sum of the first $n$ positive integers".


When Visual Studio 2010 starts up it sometimes freezes when loading documents that were previously opened when I had the solution open last. I have to end the process in Task Manager  and reopen it. When I reopen it, it skips document loading and says this in the Output window:     An error was encountered while opening associated documents the last   time this solution was loaded. Document load is being skipped during   this solution load in order to avoid that error.   My question is, is there an argument (or a setting) I can use when opening Visual Studio that will force document loading to be skipped? That way I won't have to open VS and wait for it to freeze before killing it and opening it again.

when loading up a solution in VS2008 I get:     An error was encountered while   opening associated documents the last   time this solution was loaded.   Document load is being skipped during   this solution load in order to avoid   that error.   How can I find which document is causing the problem?


Having issues with setting up the wireless network. Ubuntu system settings says that there's "No Wi-Fi Adapter Found". Downloaded the Ubuntu driver from the RealTek website but the terminal keeps giving me an error message and I'm fairly certain I'm not using the proper commands.  Posted below is the inxi -Fxz info:   System:    Host: Freedoms Kernel: 5.0.0-23-generic x86_64 bits: 64 gcc: 7.4.0            Desktop: Gnome 3.28.4 (Gtk 3.22.30-1ubuntu4)            Distro: Ubuntu 18.04.3 LTS Machine:   Device: laptop System: TOSHIBA product: Satellite C55-C v: PSCP6U-02J01E serial: N/A            Mobo: FF50 model: 06F5 v: Type2 - Board Version serial: N/A            UEFI: INSYDE v: 5.20 date: 09/15/2015 Battery    BAT1: charge: 24.6 Wh 81.9% condition: 30.0/38.5 Wh (78%)            model: Panasonic PA5185U-1BRS status: Discharging CPU:       Quad core Intel Pentium N3700 (-MCP-)             arch: Airmont rev.3 cache: 1024 KB            flags: (lm nx sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx) bmips: 12800            clock speeds: max: 2400 MHz 1: 589 MHz 2: 650 MHz 3: 1012 MHz            4: 1160 MHz Graphics:  Card: Intel Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Integrated Graphics Controller            bus-ID: 00:02.0            Display Server: x11 (X.Org 1.20.4 ) driver: i915            Resolution: 1366x768@59.99hz            OpenGL: renderer: Mesa DRI Intel HD Graphics 405 (Braswell)            version: 4.5 Mesa 19.0.2 Direct Render: Yes Audio:     Card Intel Atom/Celeron/Pentium Processor x5-E8000/J3xxx/N3xxx Series High Def. Audio Controller            driver: snd_hda_intel bus-ID: 00:1b.0            Sound: Advanced Linux Sound Architecture v: k5.0.0-23-generic Network:   Card-1: Broadcom and subsidiaries BCM43142 802.11b/g/n            bus-ID: 01:00.0            IF: N/A state: N/A mac: N/A            Card-2: Realtek RTL810xE PCIE Fast Ethernet controller            driver: r8169 port: 1000 bus-ID: 02:00.0            IF: enp2s0 state: up speed: 100 Mbps duplex: full mac: <filter> Drives:    HDD Total Size: 1004.3GB (0.9% used)            ID-1: /dev/sda model: HGST_HTS541010A9 size: 1000.2GB            ID-2: /dev/mmcblk0 model: N/A size: 15.9GB            ID-3: USB /dev/sdb model: DISK size: 4.1GB Partition: ID-1: / size: 398G used: 6.7G (2%) fs: ext4 dev: /dev/sda5 RAID:      No RAID devices: /proc/mdstat, md_mod kernel module present Sensors:   System Temperatures: cpu: 46.0C mobo: N/A            Fan Speeds (in rpm): cpu: N/A Info:      Processes: 250 Uptime: 12 min Memory: 1546.5/3854.5MB            Init: systemd runlevel: 5 Gcc sys: 7.4.0            Client: Shell (bash 4.4.201) inxi: 2.3.56     Any help would be greatly appreciated! Thank you all in advance!

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


There's a profile on Instagram where I can't see some of the persons pictures, but from my friends profile I can see them all.  The Instagram is not private. Can you do so on lyrics some people can view a specific picture?

I have a public profile on Instagram and I know about the option to make all your photos private on the service. However, I don't want to make all my photos private, but selectively make some available to the public (the rest as private). Is it possible to do so?


I'm trying to set up an sh script that will run every 30 minutes. During each run, I want to check a directory for the presence of at least one .RAW file. Upon finding that file extension, I will have other code to execute, but right now I'm having trouble figuring out the correct if statement to use.  I know this code example isn't the most ideal way to do it, but here's the code I tried which is obviously wrong:  cd ./dir/ if [ ! -f "*.RAW"]; then   echo "No files!" else   echo "Yes files!" fi   How can I correctly test for the presence of the .RAW extension?

I am trying to write an if statement to test whether there are any files matching a certain pattern. If there is a text file in a directory it should run a given script.  My code currently:  if [ -f /*.txt ]; then ./script fi   Please give some ideas; I only want to run the script if there is a .txt in the directory.


I'm trying to use cnee to record the display of a touch device we have our application on (Deployed on ubuntu server 16.04). I don't have any experience with cnee and am willing to use a different program if it is more simple to use, so please suggest any suggestions.  I've gotten cnee to record keyboard input to test it but that's it.   The command I am trying on my device is  cnee --record --display 0 -o displaytest.xns   I don't know if it makes any difference but my application is on a remote device. I'm using ssh to input the command,no log or keystrokes are needed.  I understand my command may not be doing exactly what I want but I'm trying to go off the man page, and this is the closest I've gotten to making it run after working through the error messages I was getting.

How can I record my screen on Ubuntu?   The app I'm looking for has ideally all of these features:   Can record in a format that can be played back easily on any platform and/or accepted by YouTube or another popular video site Can record just a window (instead of the whole screen), possibly selecting it with a mouse click Can start recording after a configurable delay (e.g., I launch the app and have time to do arrangements to my desktop/window before actual recording starts)


I am typesetting a paper in LaTeX:\documentclass{amsart}. I compiled it with pdflatex but the .pdf document. does not have abstract,title and key words.  Any help will be appreciated.

I'm not very good at LaTeX but I've been using it to write my dissertation. Have just come to the end and trying to format everything correctly. Whenever I try to put my Abstract paragraph into the form \begin{abstract} (writing here) \end{abstract} and click play the whole abstract section just disappears. What am I doing wrong?  \documentclass[12pt]{amsart}  \begin{document}  \begin{abstract} (my abstract here) \end{abstract} \end{document}


I have a script that conducts a Whois lookup on each domain in a list and I need to extract the creation date and the expiration date.  I have the first part but can't seem to get the expiration date also.  I don't want to run the domain through whois twice...  while IFS="," read domain rdate; do                     # Domain name and received date          cdate=( $(whois $domain | grep -m 1 -i Creation| awk -F" " '{print $3}') )                 # Harvest creation date from whois record for each domain                  # expdate=??????         printf "$domain,$cdate,$expdate \n" done < "temp1.txt" 2> /dev/null # Sets the file to read in from and suppress error messages   I tried to set the whois as "whod" like so, with no luck:  whod=$(whois $domain|awk '{print $0}') expdate=( $(echo $whod |grep -m 1 -i 'Expiration Date' | awk -F" " '{print $3}') ) echo $expdate

I'm using the following command in a script to get synthetic wifi info:  echo "$(     iw dev wlp1s0 link |     grep '^\s*SSID:\s' |     sed -r 's/^\s*SSID:\s//' ) $(     iw dev wlp1s0 link |     grep '^\s*signal:\s' |     sed -r 's/^\s*signal:\s//' )"   It works, and the output is like:  MySSID -46 dBm   However, it feels stupid to make the same call to iw dev wlp1s0 link twice, when I know that the result is going to be the same. Also, I would like to avoid having to store the output from iw in a temporary variable.  Is there something I can do, maybe using tee, to "duplicate" the output from iw to two jobs and then concatenate the results?


I have 1 dependent variable and 33 independent variables (continuous, categorical & dichotomous). Correlation analyses (2-tailed) show that the DV is only correlated to 7 of the IVs although most of the correlations are very weak, e.g. about 0.1 or less than 0.1.  Is it correct to put only IVs that are correlated with the DV into the regression model?  P.S. What's the use of the correlation matrix (1-tailed) produced with the regression analysis?

A few days ago, a psychologist-researcher of mine told me about his method to select variables to linear regression model. I guess it's not good, but I need to ask someone else to make sure. The method is:      Look at correlation matrix between all variables (including Dependent   Variable Y) and choose those predictors Xs, that correlate most with Y.     He didn't mention any criterion.  Q: Was he right?   [I think that this selection method is wrong, because of many things, like it's the theory that says which predictors should be selected, or even  omitted variable bias (OVB).]


I am going to a amusement park at the end of the month with my youth group. I will be in the car with 4 other girls and 6 boys. I need some game ideas to keep the boys busy so they won't pick on me. I'm only 14 and would need some games to play with the girls too. Thanks for your help!

I will be travelling with two kids aged 15 and 18 in a car this upcoming month, and I would like to play some games in the car with them.    I know the game where you look for different license plates, and the alphabet game where you work your way through the alphabet by looking at road signs and such. I have heard of some other games which include something called "ghost"?  where each person says one letter to try and complete a word, making sure the final letter doesn't fall on you.  Are there any other stimulating/involve the whole car type of games?


Hi, I want to find the expression of P(Y1+...+Yn>U) as shown in the screeshot below but I have no idea how to do this. I'm not sure whether I should use Erlang distribution or gamma distribution. Please advise. Any help will be greatly appreciated!

I have  that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by  describing a method for the summation of a general set of Gamma random variables. I have tried implementing  method but have yet to have success.  What does the summation of a general set of Gamma random variables look like? To make this question concrete, what does it look like for:  $\text{Gamma}(3,1) + \text{Gamma}(4,2) + \text{Gamma}(5,1)$  If the parameters above are not particularly revealing, please suggest others.


I'm just getting started with LaTeX, so likely missing something simple. I'm just looking for docs: how to get started, what commands do what, etc.  I found , but all it seems to provide is a link to a document describing differences between LaTeX 2 and 2e, neither of which I have any familiarity with.  Is there a good, online resource that acts as a kind of reference documentation for LaTeX?

Which book (free or otherwise) was the most useful to you when you started learning LaTeX?  I am frequently asked this question by friends who want to learn LaTeX, and I recommend the book which got me started, , but I feel that there might be better options around.  Also see .


I know that it the frequency of an alternating current is 50Hz.It changes its polarity 50 times. So in a circuit does the polarity gets changed these many times. It seems that it is well applicable in an ac circuit. But think of the voltage we get from the transmission lines, if we connect an iron-box to a three pin plug, does the plugs except the ground changes its polarity that many times according to the frequency.

If electrons in an alternating current periodically reverse their direction, do they really flow? Won't they always come back to the same position?