My furnace pilot light keeps going out.  The furnace will come on and heat up to the degree set on my thermostat, then the pilot goes out and the furnace will not come back on. Could the thermostat be bad and cause the pilot light to go out? Is there anyway for me to check the problem myself?
My furnace pilot light keeps going out so I changed the thermocouple. Now the furnace will come on and heat up to the degree set on my thermostat, then the pilot light will go out and the furnace will not come back on.    Could the thermostat be bad and cause the pilot light to go out?
biblatex: Full Citations in Footnotes on Every Page How can I create this sort of bibliography using biblatex, ie, bibliography at the footer of every page? Intersecting transparent object causing artifacts in cycles When two objects -one of them transparent- intersects it creates some artifacts visible even in the alpha channel. Even with 1024 transparent bounces the artifacts remain.    In the example file there are two cubes in the same position, one transparent and one emission.    What is causing this? Any way to get rid of this artifacts? Already the early papers on supergravity were written using computer algebra software to do some calculations. What modern packages do people normally use for doing such calculations? Of course Mathematica and presumable a lot of other programs can be made to do such calculations, I am wondering if there are special packages or tutorials how to do such calculations in them. showing a collection of sets contain all closed sets Let $X$ be infinite set and $a \in X $. Let $$\mathscr{F} = \{ A \subset X: |A| \; \; finite \; \;, a \notin A \}$$  Then $\mathscr{F}$ is the set all of all closed sets for some topology $\mathcal{T} $ on $X$. Also, any two continuous maps $f,g: (X, \mathscr{T}) \to Y$ ( $Y$ is metric space) have the property that if $f(b) = g(b)$ for all $b \neq a $, then $f(a) = g(a)$.  In my notes my professor posted this theorem without proof, so I was wondering what is best way to proof this theorem. A term for when people insist on giving you help you didn't ask for? People love to tell other people what to do. It may not be control, so much as trying to help, especially when you've asked for help directly. However, there's a difference between answering someone's question and answering while piling on recommendations the person didn't ask about, and this is what I'm seeking a term for. Advertising and marketing feel similar to me in this vein. In the worst cases this can be overzealous religious followers professing your damnation if you don't follow with them (I think in Christianity they call it "witnessing"). Any which way, it comes across to me as a form of unsolicited advice: I didn't ask for it, so I don't want it; I want to stay focused.  Is there a better term for this than "unsolicited advice"? Also, is there a term for a person who exhibits this kind of behavior frequently? Solving "MySQL server has gone away", mysql error 2006 Two circles intersection Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points ? How do we solve (i.e. get the closed form of) $\int \sqrt{1 + t^2} dt$ ?   shows the closed form of it but not the steps in solving it.  I think I need some algebraic trick..   I thought of some hyperbolic functions and their derivatives and equalities:  If I make $ t = \sinh x$, then I can reduce the integral to  $$ \int \cosh ^2 x dx $$ though I'm not sure if this is valid. But from here, I cannot go on evaluating the integral... Why must the eigenvalue of the number operator be an integer? My apologies if this question has already been answered. Using the notation of Sakurai, we have an energy eigenket N and an eigenvalue n.  $$N | n \rangle = n | n \rangle$$  For the number operator $N = a^\dagger a $. My question is precisely why does n have to be an integer. I do understand that it must be positive definite due to the norm condition on $ a | n \rangle $:  $$\langle n | a^\dagger a | n \rangle \geq 0$$  I can see that we can show:  $$ a | n \rangle = \sqrt{n-1} | n-1 \rangle $$ and similarly for $a^\dagger | n \rangle$  Sakurai argues that the sequential operation of $a$ operators leads to the form which he does not write, but I will write here for clarity:  $$ a^k | n \rangle = \left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right) | n - k + 1 \rangle $$   Since  $$ a|0 \rangle = 0 $$  the sequence must terminate, but can only terminate if n is an integer. How can we make that jump? Is there a formal mathematical proof that the sequence $\left(\sqrt{n}\sqrt{n-1}...\sqrt{n-k+1}\right)$ will terminate if and only if n is an integer? In the same way as you can currently render the active viewport in Open GL? Some aspects of the Workbench renderer look as if they will be very useful for NPR people. Martingale that is not a Markov process This is an exercise from Chapter 3 of Golan's linear algebra book.  Problem: Show $\mathbb{Z}$ is not a vector space over a field.  Solution attempt:  Suppose there is a such a field and proceed by contradiction. I will write multiplication $FV$, where $F$ is in the field and $V$ is an element of $\mathbb{Z}$.   First we rule out the case where the field has characteristic 2. We would have   $$0=(1_F+1_F)1=1_F1+1_F1=2$$  a contradiction.  Now, consider the case where the field does not have characteristic 2. Then there is an element $2^{-1}_F$ in the field, and   $1=2_F(2^{-1}_F1)=2^{-1}_F1+2^{-1}_F1$  Now $2^{-1}_F1\in\mathbb{Z}$ as it is an element of the vector space, but there is no element $a\in\mathbb{Z}$ with $2a=1$, so we have a contradiction.  Is this correct? Is Double-Annotating HREFLANG always alright? What if I remove one of them? How to download an MP3 track from a YouTube video How would you count occurrences of a string (actually a char) within a string? Assume you cast Barkskin in humanoid form:     You touch a willing creature. Until the spell ends, the target’s skin has a rough, bark-like appearance, and the target’s AC can’t be less than 16, regardless of what kind of arm or it is wearing.   It is clear that under the rules of Wild Shape "transforming doesn’t break your concentration on a spell you’ve already cast", but does the effect of the spell carry over to your new skin? Avoiding unused variables warnings when using assert() in a Release build How many combinations can I make? let $n \gt 1$ be an integer, and consider $n$ people; $P_1, P_2,..., P_n$ let $A_n$ be the number of ways these $n$ people can be divided into groups, such that each group have either one or two people  determine $A_1, A_2, A_3$  So I have  $A_1 = 1$ way $A_2 = 4$ way $A_3 = 12$ way  But I am not sure if this is right... Can anyone confirm?  edit:  My way of getting this is  $A_1 = 1 $ because {P1} only has 1 way to sort  $A_2 = 4$ because {P1,P2} = {P1,P2},{P2,P1},{P1P2},{P2P1}  etc. Transcendental numbers and irrationality measure Being characteristic is transitive Here, I wanted to verify that:     The property of being characteristic is a transitive relation among subgroups of a group $G$.   For subgroups $N,H\leq G$, we have $N$ char $G$ and $H$ char $N$. So $N$ char $G$ implies: $$\forall\psi\in Aut(G); \psi(N)=N$$ $H$ char $N$, so for all elements in $Aut(N)$, $H$ is remained never changing. Especially, when I take $\psi'=\psi|_{N}$ then $\psi':N\to Aut(N)$ would be in $Aut(N)$ and $\psi'(H)=H$. Since the last equality is true for $H$ and the maps, caused by restriction on $N$, then I have $H$ char $G$.  Honestly, I am inly not satisfied form the conclusion here and think I am losing something. Thanks for your hints.