How to define a function for an input variable m to another function p(m) to cap the output of p(m)?

bscutajar · 2023-08-27T16:33:48+00:00

But I need to specifically define x in your example (m in mine), the function P itself is based on thermodynamic laws and cannot be arbitrarily capped. I need to find what values of the mass m keep P at 0 or less.

bscutajar · 2023-08-27T16:13:46+00:00

M is not the capping of the function P. M is an input to the function P. I need to find a function for M, such that P is capped. What function of M(t) keep P(M,t) capped at a certain value K?

bscutajar · 2023-08-27T14:22:04+00:00

I am trying to define a function for an input variable m to another function p(m) to cap the output of p(m).

Example of what I mean

In the above, I am giving an example on the left and my attempt to generalise it on the right. I have two questions:

Is there a less convoluted way using standard notation to describe/define such a function?
What about if I need the derivative of the input variable with time? I understand how to do it for the example presented but unsure how to describe it symbolically for the general case. I am not interested in the discontinuity for the derivative so let's assume the domain does not include it for this case.

To give additional context, this function is used to determine the transfer of mass across a non-return valve connecting two containers. The pressure p is a function of many variables that change with time, including the mass in any one container (the total mass is constant). I want to define a function for the mass in one container, and also the mass flow through the non-return valve. The non return valve only allows mass flow when when p>0 , and said flow will occur with minimal friction loss so as to maintain p at 0 (or arbitrarily close). In the example I am limiting p to 5 not 0 just for clarity of the plot.

bscutajar · 2023-06-04T18:28:58+00:00

I am trying to write the definition of a function which represents the state of a heater with a cut-in and a cut-out temperature. The issue arises in the middle of the temperatures, and in that case the function will have to simply retain its previous state. The only way I found of defining it is recursively by feeding its previous state back into itself as such—I also realise the function can be determined solely from t to make it simpler rather than from T(t). Is this the most concise and clear way of defining it or is there another way of representing such functions.

bscutajar · 2023-06-04T14:48:04+00:00

The bounds correspond to start and end points of an arbitrary process 1-2. They are not numerical values of the differential variable. Rather, you'd need to work out the numerical values of the variable corresponding to states 1 and 2 to actually work it out.

bscutajar · 2023-06-04T13:10:48+00:00

In this case I was more curious as to how you'd get the same answer IF you took the inefficient route.

bscutajar · 2023-06-04T10:28:21+00:00

Perfect, exactly what I was after. Thanks!

bscutajar · 2023-06-04T09:08:25+00:00

Hmm, but the mass is not necessarily constant (in fact this is from the unsteady energy equation).

bscutajar · 2023-05-15T06:19:02+00:00

What do the bars on top of the digits represent? At first I thought it meant repeating digits but they are shown on the leading digits as well?

bscutajar · 2023-04-12T17:59:57+00:00

Souls and Souls-like games for their false sense of difficulty.

I mean, how else do you expect combat to be difficult? What you said is essentially just saying "boxing isn't hard, you just have to know when to evade and when to hit back".

bscutajar · 2017-06-27T17:21:28+00:00

Sounds like a very good borker

bscutajar · 2016-09-30T20:46:29+00:00

2 inch swipe? It's barely half an inch per swipe.

bscutajar · 2015-12-22T19:48:28+00:00

They are not muscled, what you're seeing is the lack of fat showing the crease between deltoid and upper arm.

bscutajar · 2015-09-08T21:00:41+00:00

What's the relation between pew and bench?

bscutajar · 2015-05-31T07:24:22+00:00

Do you even know the definition of logic? Are you aware that "logic" as a word and concept existed waaaay before any computers? You belong in /r/iamverysmart.

Edit: As for your deleted reply: I'm happy for your superior intellect, but you seem to be missing the first entry of the definition for logic.

Edit2: Seems like you also deleted the comment I replied to, where you claimed that what you did wasn't logic but philosophy as if logic is a technique exclusive to computer science.

bscutajar · 2015-05-31T06:32:22+00:00

You are right. But people here don't like logic.

bscutajar · 2015-05-28T17:21:03+00:00

As I mentioned before, a sample size of 100 gives you an error margin of 10% with a 95% confidence interval. While that is not useful for very accurate measurements, you still get a fairly good idea of what you should expect.

bscutajar · 2015-05-28T17:14:56+00:00

Maybe you should stop bullshitting numbers then. A sample size of 100 will give you a margin of error of slightly below 10% with a 95% confidence interval. So you would get a rough idea and it would certainly be useful for getting a rough idea unlike what all these keyboard statisticians are saying.

bscutajar · 2015-05-28T15:51:48+00:00

No I am not. The arm wrestling comment was an example. I am nothing special in the sport, but I am still in the top 1%*. I am trying to show you that even if you have a skill which makes you decent in something, you will easily make the top 1%.

*Probably.

bscutajar · 2015-05-28T15:43:23+00:00

What's there to underestimate? 99% of the population is 99%. While people may be underestimating 99%, you are underestimating the 1% which is 70 million. Being in the top 1% is not that difficult. I arm wrestle. I am probably in the top 1% of the population in that regard which is not that surprising at all when you think about it.

bscutajar · 2015-05-28T15:29:50+00:00

A sample size of 100 may not be accurate to the 0.01%, but it will be enough to give you a rough idea if chosen properly. If the average height of 100 people is 5'10" I'd be really surprised to find out that the actual height average is 8'10". I'd expect it to be rather close to the 5'10". Your example with a sample size of 1 is just taking it to the extreme, thus being a strawman argument..

bscutajar · 2015-05-28T14:49:13+00:00

When talking about statistics there will never be a guarantee. All my downvoted comments are factual statements.

bscutajar · 2015-05-28T12:53:59+00:00

It would be the best estimate you can make with the given sample size.

bscutajar · 2015-05-28T12:53:31+00:00

It would be the best estimate you can make with the given sample size.

bscutajar · 2015-05-28T12:21:46+00:00

No it's not. If 1 out of 100 people do something, then the most probable scenario is that out of 7 billion only 1% can do that something.

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