Markiyan Hirnyk

## 7198 Reputation

11 years, 270 days

## How to get asymptotic solutions?...

Maple
``` MaplePrimes member has sent you a message on MaplePrimes.

Member: faisal http://www.mapleprimes.com/users/faisal

> restart; with(PDETools), with(plots);
> n := .3; Pr := 7; Da := 0.1e-4; Nb := .1; Nt := .1; tau := 5;
> Eq1 := (1-n)*(diff(f(x, y), `\$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `\$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `\$`(y, 2)))*(diff(f(x, y), `\$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `\$`(y, 2)))*(diff(f(x, y), x)));
> Eq2 := (diff(theta(x, y), `\$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x)));
> Eq3 := Nb*(diff(phi(x, y), `\$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `\$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x)));
> ValWe := [0, 5, 10];
> bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0};
> pdsys := {Eq1, Eq2, Eq3}; for i to 3 do We := ValWe[i]; ans[i] := pdsolve(pdsys, bcs, numeric) end do;
> p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue); p2 := ans[2]:-plot(theta(x, y), x = 1, color = green); p3 := ans[3]:-plot(theta(x, y), x = 1, color = black);
> plots[display]({p1, p2, p3});```

## How to find specifications of the colors...

Of course, with Maple.

## How to implement fractal flames in Maple...

Maple

See Wiki and the description  in flame_draves.pdf for info and an example below.

## How to convert an imported data to Vect...

Maple 2016

A very big data was imported by me through

```data := Import("http://fs3.fex.net/get/245716150875/11071260/data.txt");
"3.0994584798345
22.889020258043
....

26.082759642081
42.911810680717
6.4578968130322"

```

I need to convert it to Vector/Array. Now its type is "string":

```whattype(data);
string
```

Here is my unsuccessful attempt:

```convert(data,Vector);
Error, invalid input: `convert/Vector` expects its 1st argument, V, to be of type {Array, Matrix, Vector, array, sequential}, but received 3.0994584798345
22.889020258043
....```

data.mw

## How much is "Vanity Fair"?...

Maple

What is the total number of the characters in "Vanity Fair" by William Thackeray?
How to determine it with Maple, making use of StringTools and EssayTools? I think an electronic version of this novel is free.
AFAIK, there are about 600 personages in "And Quiet Flows the Don" by Mikhail Sholokhov.

PS. It happened to me to collaborate with Dr. I. Kulchytskyi on text analysis, but the asked problem is new for me.

PPS. Here is a link to the plain text.

`Import("http://www.gutenberg.org/cache/epub/599/pg599.txt");`

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