## Spherical Bessel Functions...

Again I'm going through chapter 4 of David J. Griffiths, Introduction to Quantum Mechanics, on the section dealing with the spherical bessel functions. Can someone look at my try at a personal creation of a procedure for the spherical bessel functions and tell whether it is correct and also recommend any critiques / improvements ? the user defined procedure is called n[l]. I'm also having trouble zooming in on the plots of the spherical bessel functions created using my procedure. can anyone also help with this problem ? thanks a lot. v/r, Here is the worksheet. View 285_quantmechchapter4sphericalbessel.mw on MapleNet or Download 285_quantmechchapter4sphericalbessel.mw
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## Evaluation Rules/Problems in Maple...

I wrote a procedure that should generate a series of functions. Now I would like to integrate over the sum of a specific series of the functions. Unfortunately I can't get Maple to evaluate the last integration command even though I can plot the sum of the functions. ``` >iLk_waveform_func:=proc(Ue,Ua,Ia,L,T,t,n,k) > local liL; > # n := number of phase > # k := index of iLk > if not (t::numeric and n::numeric and k::numeric) then > return 'procname'(args) > end if; > > > if (t```

## markov model & plot a derivative function...

i create an availability function for my markov model in which use constraits like 2 maintenance tresholds and some maintenance duration, mean time between failures. i want to determine the mean time between inspections value which max. the availability and plot its graph... should i have to give exact numerical values or is there any other ways to solve it..

## Plotting point data...

I am trying to display some points on the same graph as a function. I first create 2 variables, P1:=plot(func(x),x=6..8):P2:=plots[pointplot](Data) where Data is a 10 x 2 Matrix. None of the x-values in DATA is less than 6 Problem is, when I execute plots[display]({P1,P2}) the plot produced ignores the range command in P1. It starts at x=0. Placing the range command directly in plots[display]({P1,P2}) generates an error, as does placing the range command in P2:=plots[pointplot](Data) Evidently plots[pointplot] does not accept a range command, and insists on starting at x=0. Is there any way around this?

## Time Shift and piecewise functions...

I have a piecewise defined function iL1. Now I would like to define a function iL2 = ( iL1(t+2/3*T) for 0 <= t <= 1/3*T iL1(t-1/3*T) for 1/3*T < t <= T ) How can I do this in Maple? How can I change the boundaries in a piecewise defined function in order to be able to perform a time shift? The following linked worksheet shows the definition for iL1 and what I would like to achieve. Download 305_test_piecewise_timeshift.mws

## Conflict GMP - OpenMaple...

I experienced a problem with OpenMaple: I want to use it in an application together with GMP (and other libraries) under C++. Now, when I just create gmp-integers from 1 to 100 and print them out, there is a strange behaviour if I do the same, but with starting a Maple-instance before: The numbers 8, 9 and everything greater equal 64 are not printed, instead some junk appears on the screen. But it looks like the number are internally correct, one can still calculate with them. Maybe MAPLE overwrites some global constants of GMP? Has somebody observed such problems and knows a fix? I'm using MAPLE 10, gmp-4.1.4 and gcc-3.3

## The Needleman-Wunsch algorithm for biological...

Maple

Recently I was skimming on the Internet for algorithms for alignment of biological sequences (e.g. DNA sequences, protein sequences). The usual purpose of such comparisons is to determine the evolutionary genetic history of two sequences, which in the case of DNA you can think of as strings over the alphabet {A,G,C,T} (the nucleobases). Differences between sequences can arise though substitutions (A → G, G → A, C → T, or T → C), insertions, or deletions. In the last two cases, the resulting string differs in length from the original, and dealing with these size differences is the chief problem that alignment algorithms face. The Needleman-Wunsch algorithm is a very straightforward global sequence alignment algorithm, first proposed in 1970. It's a good example of the applicability of dynamic programming towards biological problems. Following is a Maple implementation based on this Ruby implementation. The algorithm depends on a similarity matrix which measures the "mutational distance" between two nucleobases. It takes two input strings, and returns two strings with dashes ("-") inserted to indicate insertion or deletion events between the sequences.

## a number in a range...

Suppose I want to know whether or not z is in the range of 1..10. Is there any way of finding this out without writing z twice, e. g. if (z>=1) and (z

## Fieldplot in Maple 11...

I have recently upgraded to Maple 11 and I have been having a recurrent problem when I run documents with embedded plots that use "fieldplot". These documents functioned perfect using Maple 10. My problem is that I get the error "Invalid Plot Structure" when I run from a button the code restart: with(plots): plotxy:=fieldplot([x,y],x=-2..2,y=-2..2): SetProperty('Plot0', 'value', plotxy): end use; for the first time after the document is first opened. If the code is run again (after acknowledging the error, and without closing out the document), the field plot will be displayed as it should.

## solve equations...

I defined two matrices; vectorC:=Matrix(1,4,symbol=c); vectorE:=Matrix([[e],[e],[e],[e]]); so I wrote the equation: eq3:=evalm(vectorC&*vectorE)=0; I solved e as follows: solve(eq3,e); However, it shows: Error, (in solve) invalid arguments, How can I solve the problems? Thanks

## Normal Distribution Plot...

Can someone help me to plot the familiar bell shaped normal distribution curve ? I'm using the NormalPlot command with a RandomVariable, but all I'm getting is a scatter plot of points along the line, y = x. Can anyone help me to get the gaussian, bell shaped curve ? v/r,

## Piecewise Function...

I'm trying to enter a piecewise function with three parts, but can't seem to figure out how to make an extra line (the "expression" selections have one, but it only allows two lines to be entered). I read somewhere else to do CTRL+Shift+R, but that didn't seem to work. What I'm trying to enter is
y=x^2-5 x<2
-3x-7 -x<-2 and x<5
abs value(x-2) 5<x

I can get the first two lines, but can't find a way to include the third line. I'm supposed to graph the function so that all 3 are shown (may not be connected), and then I have to evaluate f(-3),f(3), and f(7). I haven't tried the evaluate part, because I can't seem to get all three components to graph. I have Maple 10. I'm new to Maple, any help would be greatly appreciated, this is quite the learning experience!