Maple Questions and Posts

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Hi everyone again

This one is linked to my previous 2 question.

Essentially I am trying to use a procedure to reproduce the formula:

S(j) = (1 + sum(H_j*T_j,j=1..n))/(1 + sum(1/(H_j*T_j),j=1..n))

BigProc:= proc(H::list,T::list)
local Form, i;
Form:=[];
for i from 1 to nops(H) do
Form := [op(Form),(1 + [sum(H[1..i]*~T[1..i],i=1..5)])/~(1 + [sum(1/~(H[1..i]*~T[1..i]),i=1..5)])]
end do:
end proc:
MainProc([1,3,5],[3,6,8])

Error, (in sum) summation variable previously assigned, second argument evaluates to 1 = 1 .. 5
 

The actual answer should be (3, 396/25,22320/509)

ie 

S(1) = (1+ 3)/(1+(1/3)) = 3

S(2) = (1 +(3+18))/(1+1/3 + 1/18)) = 396/25

S(3) = (1 +(3+18+40))/(1+1/3 + 1/18 +1/40) = 22320/509

I feel like I am missing a few things to my procedure. Any help would be greatly appreciated!

The output of a solve command was:

solution := {p[1] = 2.788944999, p[2] = 4.940143518}, { p[1] = 15.29764736, p[2] = 4.946617373}

My question is: How to capture these 4 numbers in a 2 by 2 matrix ?

I tried assign, subs commands. Did not succeed. Could some one help, please?

 

Hi

I would like to be able to use a procedure in order to create a sequence using a list. Here is an example of what I am trying to achieve:

X = [1,3,4, 50,10]

T_n = 1 + sum^n_j=1 X_j

So T_1 = 1 + 1 = 2

T_2 = 1 + [1+3] = 5

T_3 = 1 +[1+3 +4] = 9

T_4 = 1 + [1+3+4+50] = 59

T_5 = 1+ [1+3+4+50+10] = 69

So my final list would be [2,5,9,59,69]

I am quite new to this forum so i was not sure how to create the Sum from j = 1 to n bit. I know the command for creating a summation but not in a procedure sense.

How do I get a graph from Maple for function f(x) that is continuous on [0,2] except at x=1, where f(1)=4, limx approaching 1- f(x)=2, and limx approaching 1+ f(x)=3?

Duarte and Agustí (1998) investigatedthe CO2 balance o f  aquati  c ecosystems. They related thecommunity respiration rates (R) to the gross primary production rates (P) of aquatic ecosystems. (Both quantities were measured in the same units.) They made the following statement:


Our results  confirm the generality of earlier reports that the relation between community respiration rate andgross production is not linear. Community respirationis scaled as the approximate two-thirds power of grossproduction.

(a) Suppose that you obtained data on the gross production and respiration rates of a number of freshwater lakes. How would you display your data graphically to quickly convince an audience that the exponent b in the power equation relating Rand P is indeed approximately 2/3? (Hint: Use an appropriate log transformation in Maple)


(c) The r atio R/P for an ecosystem is important in assessing the global CO2 budget. If respiration exceeds production (i.e., R >P), then the ecosystem acts as a carbon dioxide source, whereas if production exceeds respiration (i.e., P > R), then the ecosystema cts as a carbon dioxide sink. Assume now that the exponent inthe power equation relating R and P is 2/3. Show that the ratio R/P, as a function of P, is continuous for P > 0. Furthermore,show that
           lim R/P =∞
            P→0+

and
            lim R/P= 0
            P→∞


How to use Maple to sketch the graph of the ratio R/P as  afunction of P for P > 0. (Experiment with the graphing calculatorto see how the value of a affects the graph.)

Hyperbolic functions are used in the sciences. The hyperbolic sine , sinh x;the hyperbolic cosine, cosh x; and the hyperbolic tangent, tanh x,defined respectively as


sinh x = ex − e−x/ 2, x ∈ R
cosh x = ex + e−x/2, x ∈ R
tanh x = ex − e−x/ex + e−x , x ∈ R


How do I show that these three hyperbolic functions are continuous forall x ∈ R using Maple?

Suppose that an organism reacts to a stimulusonly when the stim ulus exceeds a certain threshold. Assume that
the stimulus is a function of time t and that it is given by s(t) = sin(πt), t ≥ 0.The organism reacts to the stimulus and shows a certain reactio nwhen s(t) ≥ 1/2.

Define a function g(t) such  that g(t) = 0 when the organism shows no reaction at time t and g(t) = 1 when theorganism shows the reaction.

I already got the function g(t) manually.

g(t)= {  1 for 1/6 + 2k<=x<= 5/6 + 2k, k=0,1,2,...

           0  otherwise

  How do I plot s(t) and g(t) in the same coordinate system?
 

Nt+1 = RNt/ [1+ (R-1/K)Nt] where R> 1, K>0. When No >0 , lim t approaching infinityNt = K for all values of R>0.

Find Nt for t=1,2,3...10 for K= 100 and No= 20 when a) R=2, b)R=5 and c)R= 10.

I have managed to get the answers for a), b) and c) manually.

But how do I plot Nt as a function of t for the three choices of R in one coordinate system?

The pH levels of a lake controls the conc. of harmless ammonium ions(NH4+) and toxic ammonia (NH3) in the lake.

For pH levels <8, conc. of ammonium ions are little affected by pH changes, but decline over many orders of magnitude as pH levels increase beyond pH 8.

Toxic ammonia are negligible at low pH , increase over many orders of magnitude as the pH level increases and reach a high plateau at about pH =10 (after which, NH3 are little affected by pH changes).

 

How do I illustrate this graphically?

 

Percentage survivorship is a function of time; there ia negligible decline in survivorship at pH=6, marked decline in survivorship at pH=3.5, resulting in no survivors after just 8 hours.

What is the function for this problem and how do I plot it in Maple?

 

Hi all,

I have the following expression,

Typesetting[delayDotProduct](b, K[P], true)+k*K[D]-(Typesetting[delayDotProduct](b, m[1], true)+Typesetting[delayDotProduct](b, m[2], true)+K[D]*m[2])*k*K[P]/(Typesetting[delayDotProduct](b, K[D], true)+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(Typesetting[delayDotProduct](b, K[P], true)+k*K[D])/(Typesetting[delayDotProduct](b, m[1], true)+Typesetting[delayDotProduct](b, m[2], true)+K[D]*m[2]))

where K and K_P are the controller gains, k is the stiffness, b is the damper, m1 and m2 are masses.

How can I find the condition on variables such that the numerator of this expression is greater that zero?

The conditions should appear as inequalities.


 

b*K[P]+k*K[D]-(b*m[1]+b*m[2]+K[D]*m[2])*k*K[P]/(b*K[D]+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(b*K[P]+k*K[D])/(b*m[1]+b*m[2]+K[D]*m[2]))

b*K[P]+k*K[D]-(b*m[1]+b*m[2]+K[D]*m[2])*k*K[P]/(b*K[D]+k*m[1]+k*m[2]+K[P]*m[2]-m[1]*m[2]*(b*K[P]+k*K[D])/(b*m[1]+b*m[2]+K[D]*m[2]))

(1)

``


 

Download Routh-Hurwitz_stability.mw

 

The rate of resource consumption by organisms,v depends on resource concentration, S. The Blackman model of resource consumption assumes a linear relationship between v and S. Below a threshold concentration, Sk , consumption rate increases linearly with S=0 when v=0; when S=Sk, v reaches its max value, vmax. For S> Sk, v stays at vmax.

The function like this is defined piecewise,

  v= { g(S)   for 0<=S< Sk

         vmax  for S>=Sk

g(S)=( vmax/Sk).S

How do I graph v as a function of S with the graph showing the point where Sk=vmax?

Egg development

It takes 3 days at 20oC, but almost 20 days at 5oC for an egg to develop and hatch. When graphed on log -log plot, it says that egg development time (in days) as a function of temperature (in oC) is a straight line.

 

How do I sketch the log-log graph in Maple?

The chemical reaction is given as

A+2B ---> AB2

The reaction occurs ina closed vessel and the initial concentration of A=[a] and B=[b]

The reaction rate is given by

R(x)= k(a-x)(b-2x)2

where x=[AB2]

Graph R(x) for the relevant values of x when a=5,b=6 and k=0.3.

 

Need help creating a proc() for Kaprekar's routine. Ive been able to convert a number (x,n) to ascending/descending order and then defining f to be the sum of them subtracted, but i cant figure out how to put it into a proc so that it continues to loop until kaprekar's number 6174 is reached and stop.

If you have any idea please advise! thanks

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