I suppose I'm missing the point of this question: math.stackexchange.com/questions/1199089/… when students are taught about logic gates, are they not allowed to use XOR gates? (what I would have thought was the most basic of gates)
@ᴇʏᴇs I took that over my house, which I later found out is a great source of thermal turbulence. Thus, there was not much hope for the picture. This was before I knew about image stacking and before I had a decent camera. An 8" scope is capable of a much better image, but this was back when I was just starting in astrophotography.
Consider the set $M=\{(x,y)|2x+3y=0\}$, in $(R^2,||.||_2)$. Given $(x,y) \in \mathbb{R}^2$, find $P_M(x,y)$.
We've to use Gram-Schmidt orthogonal process. And how do I find the orthonormal basis e1 in M and subsequently $P_M(x,y)$. Any help will be appreciated!I'll be really grateful if anyone c...
Consider the set $M=\{(x,y)|2x+3y=0\}$, in $(R^2,||.||_2)$. Given $(x,y) \in \mathbb{R}^2$, find $P_M(x,y)$. We've to use Gram-Schmidt orthogonal process. And how do I find the orthonormal basis e1 in M and subsequently $P_M(x,y)$.
I got something but I'm not sure if it right or not?
@Dave: do you have ChatJax installed? I notice that you are not using latex, and also that David is using latex. Does what David writes appear rendered for you or as plain text?
@robjohn the major problem is that the $n$ in front doesn't have any impact on the first factors of the product, but far later on the remaining factors. Since we cannot control the first factors, we cannot find a closed form.
@robjohn The reason for that I won't work on it it's not because it is hard, but because the actual mathematics do not have solutions for the finite product I mentioned above. I'm not aware of such a product.
When $n$ is large enough we see the first factors have a word to say about the value of the limit and since they cannot be controlled, there is no sense to work on an illusion.
@robjohn I doubt any being on earth can finish that one.
The limit produces some illusions until one understands that one cannot do any progress on it without knowing the value of the product $$\prod_{k=2}^{n} (2-e^{1/k})$$
@robjohn I solved all the open problems from his book that were solvable (with one exception or so).
hello, off topic. if holomorphic functions have antiderivatives in open rectangles and discs, is there a nice way to see that they also have antiderivatives in convex open sets?
if i tke $(x_n,y_n)\rightarrow (x,y)$ i must show that $(x,y)\in A$ (x_n,y_n)\in A means that $x_n>0$ and $x_ny_n=1 $ but when i go to the limite i will obtain that $x\geq 0$ and $xy=1$ so (x,y) is not in A
@robjohn I sent one of them to AMM (some months ago).
@robjohn One of them I also showed you here on channel. The triple integral with fractional part. When I sent it to Ovidiu he told me no one sent him the solution before.
(referring to the fractional part integral)
There is an article under work with that one.
@robjohn in some cases the rigorosity level is not satisfactory enough to publish an article. I mean it's not really a good idea to send an article without clearly explaining all steps. They might not consider you a serious subscriber.
@robjohn some are intrigued by my attitude, sometimes, but there is a truth I wanna mention though, I worked incredibly crazy hard to get at this point, I cannot have small expectation from myself.
The fact that I solved the problems of Ovidiu it's only because I worked extremely hard and did a lot of research. It's not that I'm more gifted than X, Y, Z, no.
@Chris'ssis I see how you would evaluate it for small falling factorials but when you get to larger ones say $2011$, it becomes extremely difficult to evaluate. Is it then done indeirectly from there?
@Alizter For finding that one I used a new technique, say, I developed the last days. I mean I reached that point in a very curious way. You understand that when you see my proof.
@Chris'ssis I learned that the hard way. When pursuing PhD positions, I felt that drain, so I quit. That was just over a year ago. Only now, the passion has come back, and I have started maths again, buying books, contributing to MSE, loving to talk about maths.
@Lord_Farin There are so many things that create the way to success, sometimes it takes us much time to discover them.
Besides that, I'm also very ambitious, I never give up, not matter how hard is the pressure on me. I'm there ready to die than to give up. Giving up is not an option.
In general, easy is not an option.
@Lord_Farin I followed some of my dreams in the moments when no one believed in me, I was the only one that was believing in myself 100%, being alone on the way. Then, nice things began to happen. I mean I payed the price for all I got so far, I was willing to pay it.
@Lord_Farin As you mentioned, one also needs a burning passion.
@Lord_Farin I learned one important thing in the passed years: no matter what you do, try to see the beauty of the things you do. That might produce that flame of passion.
@Lord_Farin No one is perfect, people might have different expectations from us. I'm sure there are also people that appreciate and accept us the way we are, those that share the same ideas with ours.
$(x_n,y_n)\rightarrow (x,y) x_ny_n-xy=(x_n-x)y_n+x(y_n-y)\rightarrow (x-x)y+x(y-y)=0$ so $x_ny_n\rightarrow xy$ but when $x_n>0$ then $x\geq 0$ is $(x,y)\in A$ ?
@evinda I don't know. You should have something in your course that tells you what "allocation procedure" refers to. By the name, it has probably something to do with allocation, but whether it's an algorithm for allocation of memory as used in an operating system, or a given procedure that an application calls to have memory allocated, or maybe something else, I don't know.
Analytically, it's trivial @Sayan. Just multiplying by the conjugate of the numerator gives you $\frac12$, so I further question the effectiveness of the epsilon delta method...
In my notes there is the following example about the energy methhod.
$$u_{tt}(x, t)-u_{xxtt}(x, t)-u_{xx}(x, t)=0, 0<x<1, t>0 \\ u(x, 0)=0 \\ u_t(x, 0)=0 \\ u_x(0, t)=0 \\ u_x(1, t)=0$$
$$\int_0^1(u_tu_{tt}-u_tu_{xxtt}-u_tu_{xx})dx=0 \tag 1$$
$$\int_0^1 u_tu_{tt}dx=\int_0^1\frac{1}{2}(u_t^2...
see @DavidWheeler the question says prove the limit exists....i did it by taking the conjugate but i felt like using the epsilon delta proof but then i got stuck at a point
@teadawg1337 It will be hard to do that, I lost the sense of the difficulty. But, of course, it's good to take into account such an order. I try to do that.
for my taste, the straightest solution to that limit is to make an $x=\sin(2t)$ substitution (which is nicely behaved in the neighborhood of $x=0$) and observe that trig identities simplify the function to $(2\cos(t))^{-2}$.
@DavidWheeler i have these two sets $\{(x,y)\in \mathbb{R}^2, x>0, xy=1\}, B=\{(x,y)\in \mathbb{R}^2, y=0\}$ i know that these two sets are connected, closed and disjoint , and $A\cup B$ is closed because the finite union of closed sets is closed but what about the connectedness of $A\cup B$ ?
@Chris'ssis Heheeh. Did you generalise this as a function $f(x, y)$? Then you could talk about it easier. Ask AMM how long they are going to take and they reply $f(39,60)$.
@Vrouvrou are you worried that $x=0$? (it would be nice if you said this so I don't have to guess). Since the $y_n\to y$, you know that the $y_n$ are bounded, say $y_n\le M$, and so the $x_n$ are bounded away from $0$, say $x_n\ge 1/M$.
@robjohn Well, to emphasize the difference between such an answer and a brilliant answer. That thing, as I said, can be nicely done with no need of such computations.
@robjohn If you like that much I can place the result in db. :-)
@DavidWheeler I didn't understand..if we have the points $(0, n)$ and $(n, \frac{1}{n})$, then we have to prove that $\inf{d((0, n), (n, \frac{1}{n}))} = 0$
@robjohn Keep in mind this: APPLY S TO I family TO GET I family. That will explain the solution. Just remind me that when I release the book. I'll show you all the details about this way.
In my notes there is the following example about the energy methhod.
$$u_{tt}(x, t)-u_{xxtt}(x, t)-u_{xx}(x, t)=0, 0<x<1, t>0 \\ u(x, 0)=0 \\ u_t(x, 0)=0 \\ u_x(0, t)=0 \\ u_x(1, t)=0$$
$$\int_0^1(u_tu_{tt}-u_tu_{xxtt}-u_tu_{xx})dx=0 \tag 1$$
$$\int_0^1 u_tu_{tt}dx=\int_0^1\frac{1}{2}(u_t^2...
