Upper Bound for Martingale at a Stopping Time

For each $omega$, if $1 le n le tau(omega)$ then we have $|M_n-1(omega)| le h$ and so $$|M_n(omega)| le |M_n-1(omega)| |M_n(omega) - M_n-1(omega)| le h h 2h quad texta.s. $$

by your third condition. When $ell 0$ the result is trivial, and otherwise we have $1 le tau wedge ell le tau$, so applying this with $ntau(omega) wedge ell$ we get $|M_tau wedge ell| le 2h$ a.s. Squaring and taking expectations gives the desired result. (You can treat $ell0$ as a special case.)Your first condition seems to be unnecessary for this.For your last question, yes, $tau wedge ell$ is a stopping time. More generally, it is a good exercise to show that if $tau, sigma$ are stopping times then so is $tau wedge sigma$. Constants are also stopping times.

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This question seems to be quite the debate in many places. However, the general consensus falls between 3.7 and 3.85v per cell. You can find a similar inquiry here: Storing at 3.

7 or 3.

85v and here: LiPo storage voltageIt seems that generally, the difference between storage charging to 3.7v, 3.8v, or 3.85v is negligible for most people. However, I would recommend 3.7-3.8v per cell. I store my LiPos at 3.8v per cell and all of my year-old LiPos perform almost like they are brand new.The exact voltage you storage charge LiPos is important, but it is even more important that you just take good care of them and do storage charge them. It's better to storage charge LiPos to a close enough voltage than to not storage charge them at all.Here is a pretty useful guide to LiPo batteries: Guide to understanding LiPo batteries


how to truncate a line along the same slope at a given boundary?

I'd suggest you to use vector formulas and at the end unfold them to X and Y coordinates. So, the function of your line is $r_0tcdot (r_1-r_0)$ with a scalar parameter $t$, where $r_0(4,4)$ and $r_1(6,7)$. Then boundaries of your rectangle comes into play. The top boundary has equation $y5$.

$r_0ytcdot (r_1y-r_0y)5$$tfrac5-r_0yr_1y-r_0y$ (found $t$)$x$ of the intersection point $r_0xtcdot (r_1x-r_0x)$.For 4 boundaries you will have 4 intersection points. But your line obviously has 2 points of intersection with the rectangle. You chose intersection points based on the values of $t$. (Do not forget that every intersection point has a $t$ parameter.) Namely, trash 2 intersection points with the least $t$ and the greatest $t$. (I hope it is clear what I'm saying here.)


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At what angle does the stone have to be hit? duplicate

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There is not much more to say than refer to you this wiki page about the Korean Unification Flag, which also happens to be the first page you would find when googling "flag korea olympic games".The flag represents the Korean peninsula in blue on a white background. You can see it held by athletes from both Koreas in Turin 2006 Winter Olympics games on a photo in this article that confirms it will be used in 2018 as well.

Edit: As pointed in a comment by Shantanu Hebbar, the version of the Korean Unification Flag that will be used is the one without a dot for the contested Dokdo Islands (aka Takeshima, aka Liancourt) after a protest by Japanese Prime Minister Shinzo Abe. According to Wikipedia (without a source for this claim), Ulleungdo Island will not figure either, so it should be this version of the flag


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The specific case of email really depends on your pair: some just don't care, some expect you to look away, some will read email during a break so you don't have a chance to see it, and so on


Is this attempt at a case-study question something we'd like to see more of?

If it is a literary critique, I would vote to close as too localized if not off-topic. If it is a literary analysis then it's a different story.I would like when people show what (they think) works or does not work using a concrete example. However, a disadvantage is that only a minority knows the books in question, which restricts the number of people who can answer the question. Nevertheless I would give it a try.But to your "guidance" in your question:That's a bad idea. Meta Stack Overflow works this way and many people do not get it, do not want to understand it and love their rep much too much. Getting a downvote because stating one's opinion will drive people away. Meta.SO is only a meta site, so losing some people there does not hurt, but we shouldn't do that


Should a new programmer focus on a single technology until he's proficient at it? closed

It's not bad if he is a beginner in programming.He will see how some stuff work's. But if he doesen't understand the what he is doing it's better not to do it at all.I had that problem with myself i want to know it all Java, C, C, C#, Phyton, ASP.NET...etc

but i realized i can't know it all, so i focused on couple of things's and it's much better.So what should he do(advise him):I would not agree with @arnaud if you always explore and learn new stuff when a new project is in front of you(well not completely).

It takes too much time to explore and learn new stuff again and again and some projects have a time limit. But on the other hand if you need to learn some simple new stuff it's ok :D .


CPU Constantly at 100% In Task Manager, But Not in Process Explorer

Before, I used to be able to change the power settings like Andrew M had said. The fix that originally worked for me was to change my performance plan. Ex going from High Performance to Power Saver. Windows 10 >> Right click desktop >> DISPLAY SETTINGS >> (under system tab) POWER & SLEEP >> (Related Settings) Additional Power Settings. Or Go to "Ask Me Anything"/Cortana ( the start menu search feature and type in... "Power Options".OR EASIEST WAY ---> Right click the windows 10 logo/start button. Click "Power Options".

I could swap between high performance and power saving and it would reset by itself, but for some reason when I opened skype the fans came on blazing and it would not go below 100%, so I did my method and it didnt change anything this time, ended up finding this backdoor/work-around. Works great, thank you. Andrews Response worked for me

Upper Bound for Martingale at a Stopping Time 1

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