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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At what voltage per cell should I store a LiPo?

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

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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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Entropy at zero kelvin for pure atom crystal

You seem to underline some perceived inherent difference between water and elemental compounds. There is none. A crystal of water ice, so to put it, is as crystalline as any other crystal.There are quite a few crystals (indeed, certain elemental compounds are among them) that exhibit some kind of disorder; as you lower the temperature, their molecules (or atoms, or ions) freeze in somewhat different positions having nearly the same energy, so if you extrapolate to zero, you'll see that they retain some significant entropy even then. This has nothing to do with the Third law. These crystals are not ideal by a wide margin, and they are not going to become more ideal anytime soon, especially if you keep them near the absolute zero.On a side note, the words "practice" and "at 0 K" do not sit well together, but that's another story.

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What can I cure at 15c and 50% humidity?

This is pretty close to the temperature and humidity of the closet where I store wine and hang salumi to cure. I've had the most success with pancetta, lomo, and brasola. I've had some successes and some failures with dried sausages and salami, usually related to undesirable mold that I didn't catch in time. I probably wouldn't hang an entire pork leg, in an effort to make something like a prosciutto. Generally, because of the cost and labor involved, I would want the conditions to be more precise and less variable. In my wine closet, the temp and humidity does change. However, for the smaller items I am playing with, and given the time necessary, the conditions are just fine. It sounds like a reasonable place to experiment. One final note, be sure your space is insect and rodent-free. That could be a potential issue.

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How to prove that any line contain at least three points?

This is a strange definition, and not the normal set of axioms I usually see. It is possible that, for whatever reason, the author wants to include degenerate cases, such as the empty space, a single point, or a line with two points.Maybe you can give the rest of the definition, instead of just the axioms? For example, I find it odd that planes are referred to in these axioms. Are these axioms explicitly for a projective 3-space?One set I usually see for projective plane/space is:(Although if you want to talk more generally about a projective geometry there may be reasons you don't want to exclude the projective line. Also you sometimes want to explicitly include all of the subgeometries of each dimension as objects that are part of the geometry, instead of defining them in terms of points and lines.)

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

Within a total angle of $4arcsinfrac5.5(12times87)5.5$ or approximately 1 degree 12 minutes 3.8175 seconds. It should be noted that the configuration shown in your diagram cannot be attained without curling the path of the moving stone, because when the two stones become tangent at the furthest extent of the possible contact angle, the center of the moving stone is not yet up to the line that you have the three tangent stones shown at. At the point when the moving stone is going to be minimally tangent to the stationary stone the distance between the point of release and the center of the moving stone should equal the distance between the point of release and the center of the target stone. 87 feet 5.5 inches, in other words. The 5.5 inches is the radius of a stone, of course.By the way, from what part of Canada are you?.

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$6$ persons stand at random in a queue for buying cinema tickets individually

If $F$ denotes a person with five rupee note and T denotes the person with a ten rupee note, then we need arrangements such that the number of F is more than the number of T at any point in the queue. This is equivalent to finding the number of paths from the lower left corner to the upper right corner in the figure that lies below the diagonal line. Counting the number of ways or reaching each grid point, the number of favorable cases is 5.

Arrangements of 6 persons in the queue is $frac6!3!3!$, since we are interested only in all getting tickets. Thus the probability is $frac520 frac14$.More generally, if there are $n$ persons with five rupee notes and $n$ persons with ten rupee notes, then the number of favorable cases is $frac1n1binom2nn$, the $n$ th Catalan number.

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Which flag will North and South Korea march under at the Olympic games?

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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What's the etiquette on looking at the other person's email when pair programming?

There is no general rule: you have to discuss it with your pair.Pair-programming is a pretty invasive practice. You do not decide to invite a colleague into your private space to discuss something. Instead, you are supposed to give up your private space and share your desktop, screen, thoughts, on a regular basis: you work very close to each other. You set up rules along the way by telling your pair what he / she can do and what not. For each pair it is different. Some pairs work well together from day 1, some pairs take weeks or months to find common rules, some never do.

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

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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

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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 .

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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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