Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 Re: Help Me ! » S-shaped function » 2016-04-28 11:06:19

Hi Bobbym,
Something like this picture.
http://i60.tinypic.com/2ykbz2v.png
I'd like to have a numerical formula by which I can define a desirable S_shaped curve (desired minimum, maximum, slope).

Thank you

## #2 Help Me ! » S-shaped function » 2016-04-28 09:26:07

kappa_am
Replies: 3

Hi fellas,
I need an S-shaped function whose starting point (t), steepness, starting value(y1), and end value (y2) can be adjustable.
I would be grateful if you provide me with a numerical solution or a formula.

Thanks

Done!

## #4 Re: Help Me ! » Discrete mathematics » 2016-01-10 19:30:40

for example suppose my set is 1 1 2 2. if second switch fails the set turn to 1 3 2. there is 1 switch less than or equal to 2^0, two switch LE 2^1 and 3 switches LE 2^2. so first condition is satisfied. Second condition is also satisfied. So, it works.
Now, suppose third switch fails; the set will be 1 1 4. there is 1 switch LE 2^0, two switch LE 2^1 and 3 switches LE 2^2. so first condition is satisfied. But since 4>6/2. this series cannot provide all levels ( numbers between 1 to 6).

Since I have develop this method by thinking and try&error, I am not sure about it. Please inform me if this method has any defect. Thank you

## #5 Re: Help Me ! » Discrete mathematics » 2016-01-10 17:16:01

I kid of thinking of a solution. Lets suppose my system has M modules. each with voltage Vm. I think the system can maintain its functionality if the following conditions are true. I am not sure, please confirm.

1- for every K ( K is a number from 1 to M), there are K number of switch with weight less than 2^K
2-weight of the next switch to the failed switch, after adding weight of failed switch weight to it remain less than half of the summation of all members.

Does it work?
I am afraid, but I do not know what SE stand for.

## #6 Re: Help Me ! » Discrete mathematics » 2016-01-10 16:47:02

yes. means the system has up to 25 sub-modules.

## #7 Re: Help Me ! » Discrete mathematics » 2016-01-10 13:49:45

up to 20-25. However, a general formula is more desired.

## #8 Re: Help Me ! » Discrete mathematics » 2016-01-10 11:55:23

actually this is a fault tolerant inverter, in which if a sub-module failed. the other modules try to maintain the performance using appropriate control. This is first step to examine that the remained operating circuit can compensate loss of that sub-module or not. Therefore, yes, simple as much as possible.

## #9 Re: Help Me ! » Discrete mathematics » 2016-01-10 11:24:31

it is MOSFET, controlled by micro controller.

## #10 Re: Help Me ! » Discrete mathematics » 2016-01-10 09:38:46

No, they can be any  positive integer number. But the failed switch is discriminated (provided by fault diagnosis system).

Enjoy your meal

## #11 Re: Help Me ! » Discrete mathematics » 2016-01-10 09:05:58

We have a series in which each number is per-unit voltage of a inverter. We have several inverters connected series to each other generating output voltage ( it look like a staircase waveform). for example 1, 1, 2, 2 means I have 4 inverter 2 with voltage 1V (per-unit) and 2 with 2V. by this inverters I can produce voltage levels from 1 up to 6. suddenly one of the inverters fails. the connection is in such a way that weight of the failed switch transfers to upper switch. suppose the third switch fails the series turns to 1, 1, 4. first I have to examine that am I able to generate all levels or not. then proceed to appropriate program. in this case I can not generate all levels. Because there is no way to generate 3.

Thanks for all your helps

## #12 Re: Help Me ! » Discrete mathematics » 2016-01-10 08:47:54

dsPIC30F4011. What I need is that I have to ensure that by existing number, all numbers up to summation of all members can be construct. no need to find specific number. There has to be a simple rule.
like the next number in the series be less than summation of the previous numbers. I thought a lot, but every way has a defect!!

P.S I need the answer (yes or no) in less than 10us.

## #13 Re: Help Me ! » Discrete mathematics » 2016-01-10 08:31:17

I got it. Thank you. math is always fascinating.
I need to implement this method to control a procedure (physical). It seems this requires heavy computation. Do you have any recommendation in programming this algorithm? our micro has limited computation power and I need to have efficient algorithm.

## #14 Re: Help Me ! » Discrete mathematics » 2016-01-10 06:30:31

could you explain more or introduce me a reference.
your help is appreciated.

## #15 Help Me ! » Discrete mathematics » 2016-01-09 20:50:41

kappa_am
Replies: 29

Hi,
I have a question about series (some members are repeated). I have a series, How can I find out if this series make all numbers up to summation of all members. Is there any formula?

for example {1, 1, 2, 4}; the subsets of this set can construct all numbers from 1 to 8.
{0, 1, 3, 4} cannot make all numbers ( 2 and 6 cannot be constructed).

question is how determine that if a set is capable to construct all numbers up to all members summation or not. a general formula would be appreciated.

Thank you.

## #16 Re: Help Me ! » Curve fitting » 2015-05-21 19:53:30

it steady on 1 after 165, I have examined over 10 points.

## #17 Re: Help Me ! » Curve fitting » 2015-05-20 20:34:54

yes it comes from an experiment. least squares is ok.

thank you

## #18 Help Me ! » Curve fitting » 2015-05-19 22:21:06

kappa_am
Replies: 5

Hi all;
I need to find a function that fit to all the obtained points. I used MATLAB curve fitting, and found some function. However there is a problem. Most of the proposed function by Matlab rapidly increases or decreases, while my other point which are not engaged in curve fitting are constant and equal to 1. I would be grateful if you suggest me a method to find a most suitable function.

The data is  as below:
x
55
65
75
85
95
105
115
125
135
145
155
165

Y

0.030
0.077
0.143
0.393
0.595
0.821
0.940
0.964
0.988
0.988
0.994
1.000

Thank you

## #19 Re: Help Me ! » writing in formal language » 2015-04-18 01:33:51

this is a engineering work, and may be a little different from pure mathematics. the member of the set is defined by number of the power converter those may have equal output voltage (same value in the set).

another question is that can not we show a set of mod n as ℤn?

## #20 Help Me ! » writing in formal language » 2015-04-17 20:37:07

kappa_am
Replies: 2

hi all,
I would like to write following expression using math symbols. since my study branch is not mathematics I am a little confused. I would be grateful if someone help me.

I like to say: set A is subset of integer mod N (N= 2^|A|) and there are at least M member of set A that are smaller than or equal to 2^(M-1)

for example: A={1, 2, 3, 3}. it is subset of integer mod 16 and there are 1 member <= 2^0 , 2 member <= 2^1, 4 member <= 2^2 and 4 member <= 2^3.

how can write this in formal language?

thank you

## #21 Re: Help Me ! » Permutation » 2014-04-08 04:54:44

at least one 1 has to be in series because if it not be, I haven't any subset that its value is 1. this is general.
but 6 is for this specific example (x=9, N=4), because if 6 is in set all other member have to be 1 (minimum value). but in this situation I haven't any subset that add up to 4 and 5.

if x was 12 then 6 could be in series like (1,2,3,6).

I think if we could find a relationship for determining maximum value for each problem using N and X we could find the number of sets that satisfy the mentioned conditions.
Am I right?

## #22 Re: Help Me ! » Permutation » 2014-04-08 04:38:34

yes, the list is ok! just the sets that haven't any 1 and sets that have 6 have to be obliterate.
(6 1 1 1), (1 6 1 1), (1 1 6 1), (1 1 1 6), (2 3 2 2), (2 2 3 2), (2 2 2 3), (3 2 2 2) have to be obliterated.
I like a formula by having X and N, the number of sets can be obtained. it it obvious that at least one of rooms has to be 1. if we can find a rule for maximum number we may be able to find a  formula.
the highest number for this example is 5. it has relationship with N and X. I am trying to develop a rule for maximum number. I think after that we could develop a rule for obtaining the number of sets.

## #23 Re: Help Me ! » Permutation » 2014-04-08 04:10:30

we can generate ,but we cannot generate 4 and 5 of this set 6,1,1,1
we cannot generate 1 of subsets that haven't any 1 like 2,2,3,2

## #24 Re: Help Me ! » Permutation » 2014-04-08 03:55:19

sorry, I write it vague.
let me clarify:
I have X and N number of rooms
here are the conditions:
summation of all N number have to be X
and all integer number less than X ([1 X-1]) should be obtained using at least one subset of those numbers.
I can obtain 1 of any series that have at least one 1 in that.

## #25 Re: Help Me ! » Permutation » 2014-04-08 02:15:13

there is a condition all numbers up to x=9 could be obtained using the series member but: we cannot generate 4 using 6,1,1,1 or I cannot generate 1 using 2,2,3,2...
some members have to be obliterated.
according to above condition at least one room has to be 1.

Thank you for taking time to help me.

## Board footer

Powered by FluxBB